input output machinery

machine | britannica

machine | britannica

Machine, device, having a unique purpose, that augments or replaces human or animal effort for the accomplishment of physical tasks. This broad category encompasses such simple devices as the inclined plane, lever, wedge, wheel and axle, pulley, and screw (the so-called simple machines) as well as such complex mechanical systems as the modern automobile.

The operation of a machine may involve the transformation of chemical, thermal, electrical, or nuclear energy into mechanical energy, or vice versa, or its function may simply be to modify and transmit forces and motions. All machines have an input, an output, and a transforming or modifying and transmitting device.

Machines that receive their input energy from a natural source, such as air currents, moving water, coal, petroleum, or uranium, and transform it into mechanical energy are known as prime movers. Windmills, waterwheels, turbines, steam engines, and internal-combustion engines are prime movers. In these machines the inputs vary; the outputs are usually rotating shafts capable of being used as inputs to other machines, such as electric generators, hydraulic pumps, or air compressors. All three of the latter devices may be classified as generators; their outputs of electrical, hydraulic, and pneumatic energy can be used as inputs to electric, hydraulic, or air motors. These motors can be used to drive machines with a variety of outputs, such as materials processing, packaging, or conveying machinery, or such appliances as sewing machines and washing machines. All machines of the latter type and all others that are neither prime movers, generators, nor motors may be classified as operators. This category also includes manually operated instruments of all kinds, such as calculating machines and typewriters.

In some cases, machines in all categories are combined in one unit. In a diesel-electric locomotive, for example, the diesel engine is the prime mover, which drives the electric generator, which, in turn, supplies electric current to the motors that drive the wheels.

As part of an introduction to machine components, some examples supplied by an automobile are of value. In an automobile, the basic problem is harnessing the explosive effect of gasoline to provide power to rotate the rear wheels. The explosion of the gasoline in the cylinders pushes the pistons down, and the transmission and modification of this translatory (linear) motion to rotary motion of the crankshaft is effected by the connecting rods that join each piston to the cranks that are part of the crankshaft. The piston, cylinder, crank, and connecting rod combination is known as a slider-crank mechanism; it is a commonly used method of converting translation to rotation (as in an engine) or rotation to translation (as in a pump).

To admit the gasolineair mixture to the cylinders and exhaust the burned gases, valves are used; these are opened and closed by the wedging action of cams (projections) on a rotating camshaft that is driven from the crankshaft by gears or a chain.

In a four-stroke-cycle engine with eight cylinders, the crankshaft receives an impulse at some point along its length every quarter revolution. To smooth out the effect of these intermittent impulses on the speed of the crankshaft, a flywheel is used. This is a heavy wheel, attached to the crankshaft, that by its inertia opposes and moderates any speed fluctuations.

Since the torque (turning force) that it delivers depends on its speed, an internal-combustion engine cannot be started under load. To enable an automobile engine to be started in an unloaded state and then connected to the wheels without stalling, a clutch and a transmission are necessary. The former makes and breaks the connection between the crankshaft and the transmission, while the latter changes, in finite steps, the ratio between the input and output speeds and torques of the transmission. In low gear, the output speed is low and the output torque higher than the engine torque, so that the car can be started moving; in high gear, the car is moving at a substantial speed and the torques and speeds are equal.

The axles to which the wheels are attached are contained in the rear axle housing, which is clamped to the rear springs, and are driven from the transmission by the drive shaft. As the car moves and the springs flex in response to bumps in the road, the housing moves relative to the transmission; to permit this movement without interfering with the transmission of torque, a universal joint is attached to each end of the drive shaft.

The drive shaft is perpendicular to the rear axles. The right-angled connection is usually made with bevel gears having a ratio such that the axles rotate at one-third to one-fourth the speed of the drive shaft. The rear axle housing also holds the differential gears that permit both rear wheels to be driven from the same source and to rotate at different speeds when turning a corner.

Like all moving mechanical devices, automobiles cannot escape from the effects of friction. In the engine, transmission, rear axle housing, and all bearings, friction is undesirable, since it increases the power required from the engine; lubrication reduces but does not eliminate this friction. On the other hand, friction between the tires and the road and in the brake shoes makes traction and braking possible. The belts that drive the fan, generator, and other accessories are friction-dependent devices. Friction is also useful in the operation of the clutch.

Some of the devices cited above are found in machines of all categories, assembled in a multitude of ways to perform all kinds of physical tasks. The function of most of these basic mechanical devices is to transmit and modify force and motion. Other devices, such as springs, flywheels, shafts, and fasteners, perform supplementary functions.

A machine may be further defined as a device consisting of two or more resistant, relatively constrained parts that may serve to transmit and modify force and motion in order to do work. The requirement that the parts of a machine be resistant implies that they be capable of carrying imposed loads without failure or loss of function. Although most machine parts are solid metallic bodies of suitable proportions, nonmetallic materials, springs, fluid pressure organs, and tension organs such as belts are also employed.

The most distinctive characteristic of a machine is that the parts are interconnected and guided in such a way that their motions relative to one another are constrained. Relative to the block, for example, the piston of a reciprocating engine is constrained by the cylinder to move on a straight path; points on the crankshaft are constrained by the main bearings to move on circular paths; no other forms of relative motion are possible.

On some machines the parts are only partially constrained. If the parts are interconnected by springs or friction members, the paths of the parts relative to one another may be fixed, but the motions of the parts may be affected by the stiffness of the springs, friction, and the masses of the parts.

If all the parts of a machine are comparatively rigid members whose deflections under load are negligible, then the constrainment may be considered complete and the relative motions of the parts can be studied without considering the forces that produce them. For a specified rotational speed of the crankshaft of a reciprocating engine, for example, the corresponding speeds of points on the connecting rod and the piston can be calculated. The determination of the displacements, velocities, and accelerations of the parts of a machine for a prescribed input motion is the subject matter of kinematics of machines. Such calculations can be made without considering the forces involved, because the motions are constrained.

production function type: 3 main types of production functions | managerial economics

production function type: 3 main types of production functions | managerial economics

In economic theory, we are concerned with three types of production functions, viz.:- 1. Production Functions with One Variable Input 2. Production Function with Two Variable Inputs 3. Production Function with all Variable Inputs.

If one input is variable and all other inputs are fixed, the firms production function exhibits the law of variable proportions. If the number of units of a variable input is increased, keeping other inputs constant, how output changes is the concern of this law. Suppose land, plant, and equipment are the fixed factors, and labor the variable factor. When the number of laborers is increased successively to have larger output, the proportion between fixed and variable factors is altered and the law of variable proportions sets in.

The law states that as the quantity of a variable input is increased by equal doses, keeping the quantities of other inputs constant, total product will increase, but after a point, at a diminishing rate. This principle can also be defined thus When more and more units of the variable factor are used, holding the quantities of fixed factors constant, a point is reached beyond which the marginal product, then the average, and finally the total product will diminish.

The law of variable proportions (or the law of non-proportional returns) is also known as the law of diminishing returns. But, as we shall see below, the law of diminishing returns is only one phase of the more comprehensive law of variable proportions.

An analysis of Table 3.3 shows that the total, average, and marginal products increase at first, reach a maximum when seven units of labor are used and then it declines. The average product continues to rise till the fourth unit while the marginal product reaches its maximum at the third unit of labor, then they also fall.

The marginal product starts declining first, then the average product, and finally the total product. It should be noted that the point of falling output is not the same for total, average, and marginal product. This observation points out that the tendency to diminishing returns is ultimately found in the three productivity concepts.

The law of variable proportions is presented diagrammatically in Fig. 3.11. The TP curve first rises at an increasing rate and then reaches the highest point at a decreasing rate and then starts falling slowly. The slope of the TP curve at any point can be known by drawing a tangent at that point. In Fig. 13.11, there are three such points. At point a the slope of TP is the highest, at b it is less than a and at c it becomes zero. The marginal product curve (MP) and the average product curve (AP) also rise with TP.

The MP curve reaches its maximum point d when the slope of the TP curve is the maximum at point a and then starts falling. The maximum point on the AP curve is e where it coincides with the MP curve. This point also coincides with b on the TP curve from where the total product starts a gradual rise.

When the TP curve reaches its maximum point c, the MP curve becomes zero at point f, and when the former starts declining, the latter becomes negative. It is only when the total product is zero that the average product also becomes zero. The rising, the falling, and the negative phases of the total, marginal, and average products are in fact the different stages of the law of variable proportions.

In Stage I, the average product reaches the maximum and equals the marginal product when four workers are employed, as shown in Table 3.3. In this stage, the total product curve also increases rapidly. Thus, this stage relates to increasing average returns. Here, land is too much in relation to the workers employed. It is, therefore, uneconomical to cultivate land in this stage.

The main reason for increasing returns in the first stage is that in the beginning the fixed factors are larger in quantity than the variable factors. When more units of variable factors are applied to a fixed factor, the fixed factor is used more intensively and production increases rapidly.

It can also be explained in another way. In the beginning, the fixed factor cannot be put to the maximum use due to the non-applicability of sufficient units of variable factors. But when units of variable factors are applied in sufficient quantities, division of labor and specialization lead to per unit increase in production and the law of increasing returns operates.

Production cannot take place in Stage III either. For, in this stage, total product starts declining and the marginal product becomes negative. The employment of the eighth worker actually causes a decrease in total output from 60 to 56 units and makes the marginal product 4.

In the figure, this stage starts from the dotted line of where the MP curve is below the X-axis. Here the workers are too many in relation to the available land, making it absolutely impossible to cultivate it.

When production takes place to the left of point e, the fixed input is in excess quantity in relation to the variable input. To the right of point f, the variable input is used excessively. Therefore, production will always take place within these stages.

In between Stages I and III is the most important stage of production that of the law of diminishing returns. Stage II starts when the average product is at its maximum to the zero point of the marginal product. At the latter point, the total product is the highest. Table 3.3 shows this stage when the workers are increased from four to seven to cultivate the given land. In the figure, it lies between be and cf.

Here land is scarce and is used intensively. More and more workers are employed in order to have a larger output. Thus, the total product increases at a diminishing rate and the average and marginal products decline. Throughout this stage, the marginal product is below the average product. This is the only stage in which production is feasible and profitable.

6. The product is measured in physical units, i.e., in quintals, tonnes, etc. The use of money in measuring the product may show increasing rather than decreasing returns if the price of the product rises, even though the output may have declined.

The last segment of the theory of production is the problem of determining the least- cost combination of factors for a given output. The aim of every producer is to get maximum profits, and to achieve this he combines the various resources in such a proportion that a given output is manufactured at the least cost.

This problem is similar to the problem faced by the consumer who allocates his money income among several commodities for obtaining maximum satisfaction. The consumer is in equilibrium when the marginal utilities and the price ratios of the goods bought become equal.

To achieve this equilibrium position, the consumer acts on the principle of substitution. Similarly, the producer will be in equilibrium when the marginal productivities of the various factor units employed by him are equal to their prices. To achieve the least-cost combination of a given output, he substitutes a cheap input for a costly input.

If he finds that the marginal product of a rupees worth of factor A is greater than that of factor B, he will spend less on B and more on A. He will continue to spend like this with the consequence that the marginal product of a rupees worth of factor B will steadily rise, while that of factor A will fall, until the least-cost combination is achieved.

Suppose that a producer uses three inputs A, B, and C in the production of commodity X. The price of A is Rs.3 per unit, of B Rs.2 per unit, and of C Rs.1 per unit. The cost outlay on the three factors is Rs.61 per day. The daily marginal productivities of the different units of these factors resources are shown in Table 3.4.

The price (Pa) of A being Rs.3 per unit, of B (Pb) Rs.2 per unit, and that of C (Pc) Rs.1 per unit, in equilibrium the marginal product of A (M Pa) should be 1.5 of B (M Pb) and twice that of C (M Pc). When the consumer continues to use more units of factors A, B, and C to produce a fixed quantity of X (columns 1, 3, 5 of the table, their marginal productivities continue to decline (columns 2, 4, 6).

Ultimately, the equilibrium position is reached when the marginal productivity of factor A (M Pb = 6) and the marginal productivity of B is twice that of C (M Pc = 3). This position is attained at 9 units of A, 11 units of B, and 12 units of C, where the marginal product per rupees worth of each input is equalized.

Another condition for the least-cost combination is that the entire cost outlay for the given period should be fully spent at the level of equilibrium. This condition is also satisfied at the above combination of 9 units of A, 11 units of B, and 12 units of C. This is shown below.

If a combination, other than the above is taken, the two conditions will not be satisfied. Suppose Re.1 is withdrawn from input B and spent on input C, it will mean loss of 3 units and an addition of only one unit when the thirteenth unit of C is acquired. This reallocation leads to a fall in the firms total product by two units. The producer is also not in a position to utilize the entire cost outlay. He spends Rs.1 less than before

The principle of least-cost combination also implies that each factor unit will be so employed as to equate its marginal product per rupees worth in every use or occupation. If the marginal product of labor is greater in cotton textile industry than in the jute industry, labor will move from the latter to the former till marginal productivity of labor becomes equal in both the industries. Equality between different units of capital, labor, etc., is also established in a similar manner.

To conclude, the principle of least-cost combination is an important tool in production theory. It points out that the efficient combination of variable factors which the producer should use depends upon the marginal productivities and prices of the respective factors.

To understand a production function with two variable inputs, it is necessary to explain what an isoquant is. An isoquant is also known as iso-product curve or equal-product curve or a production-indifference curve. These curves show the various combinations of two variable inputs resulting in the same level of output. Table 3.5 shows how different pairs of labor and capital result in the same output.

Thus, by graphing a production function with two variable inputs, one can derive the isoquant tracing all the combinations of the two factors of production that yield the same output. An isoquant is defined as the curve passing through the plotted points representing all the combinations of the two factors of production which will produce a given output.

An important assumption in the isoquant diagram is that the inputs can be substituted for each other. Let us take a particular combination of X and Y resulting in an output Q 600, one finds other quantities of the inputs resulting in the same output. Let us suppose that X represents labor and Y, machinery. If the quantity of the labor (X) is reduced, the quantity of machinery (Y) must be increased in order to produce the same output.

The slope of the isoquant has a technical name- marginal rate of technical substitution (MRTSw), or sometimes, the marginal rate of substitution in production. Thus, in terms of inputs of capital services K and labor L.

In this type, there is perfect substitutability of inputs. For example, a given output say 100 units can be produced by using only capital or only labor or by a number of combinations of labor and capital, say 1 unit of labor and 5 units of capital, or 2 units of labor and 3 units of capital, and so on.

Likewise, given a power plant equipped to burn either oil or gas, various amounts of electric power can be produced by burning gas only, oil only, or varying amounts of each. Gas and oil are perfect substitutes only, oil only, or varying amounts of each. Gas and oil are perfect substitutes here. Hence, the isoquants are straight lines (See Fig. 3.13).

In this type, there is complete non-substitutability between the inputs (or strict complementarity). For example, exactly two wheels and one frame are required to produce a bicycle and in no way can wheels be substituted for frames or vice-versa. Likewise, two wheels and one chassis are required for a scooter. This is also known as Leontief isoquant or input-output isoquant (See Fig. 3.14).

This form assumes substitutability of inputs but the substitutability is not perfect. For example, a shirt can be made with relatively small amount of labor (L1) and a large amount of cloth (C1). The same shirt can be as well made with less cloth (C2), if more labor (L2) is used because the tailor will have to cut the cloth more carefully and reduce wastage.

Finally, the shirt can be made with still less cloth (C3) but the tailor must take extreme pains so that labor input requirement increases to L3. So, while a relatively small addition of labor from L1 to L2 allows the input of cloth to be reduced from C1 to C2, a very large increase in labor from L2 to L3 is needed to obtain a small reduction in cloth from C2 to C3. Thus, the substitutability of labor for cloth diminishes from L1 to L2 to L3.

1. An isoquant is downward sloping to the right, i.e., negatively inclined. This implies that for the same level of output, the quantity of one variable will have to be reduced in order to increase the quantity of other variable.

3. No two isoquants intersect or touch each other. If two isoquants intersect or touch each other, this would mean that there will be a common point on the two curves; and this would imply that the same amount of two inputs can produce two different levels of output (i.e., 400 and 500 units) which is absurd.

4. Isoquant is convex to the origin. This means that its slope declines from left to right along the curve. In other words, when we go on increasing the quantity of one input, say labor by reducing the quantity of other input, say capital. We see that less units of capital are sacrificed for the additional units of labor.

1. If the proportional increase in all inputs is equal to the proportional increase in output, returns to scale are constant. For instance, if a simultaneous doubling of all inputs results in a doubling of production, then returns to scale are constant (Fig. 3.16).

The increasing returns to scale are attributable to specialization. As output increases, specialized labor can be used and efficient large-scale machinery can be employed in the production process. However, beyond some scale of operations not only are further gains from specialization limited, but also co-ordination problems may begin to increase costs substantially. When coordination costs more than offset additional benefits of specialization, decreasing returns to scale begin.

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The first layer in a CNN is always a Convolutional Layer. First thing to make sure you remember is what the input to this conv (Ill be using that abbreviation a lot) layer is. Like we mentioned before, the input is a 32 x 32 x 3 array of pixel values. Now, the best way to explain a conv layer is to imagine a flashlight that is shining over the top left of the image. Lets say that the light this flashlight shines covers a 5 x 5 area. And now, lets imagine this flashlight sliding across all the areas of the input image. In machine learning terms, this flashlight is called a filter(or sometimes referred to as a neuron or a kernel) and the region that it is shining over is called the receptive field. Now this filter is also an array of numbers (the numbers are called weights orparameters). A very important note is that the depth of this filter has to be the same as the depth of the input (this makes sure that the math works out), so the dimensions of this filter is 5 x 5 x 3. Now, lets take the first position the filter is in for example. It would be the top left corner. As the filter is sliding, or convolving, around the input image, it is multiplying the values in the filter with the original pixel values of the image (aka computing dot products). These multiplications are all summed up (mathematically speaking, this would be 75 multiplications in total). So now you have a single number. Remember, this number is just representative of when the filter is at the top left of the image. Now, we repeat this process for every location on the input volume. (Next step would be moving the filter to the right by 1 unit, then right again by 1, and so on). Every unique location on the input volume produces a number. After sliding the filter over all the locations, you will find out that what youre left with is a 28 x 28 x 1 array of numbers, which we call an activation map or feature map. The reason you get a 28 x 28 array is that there are 784 different locations that a 5 x 5 filter can fit on a 32 x 32 input image. These 784 numbers are mapped to a 28 x 28 array.

Lets say now we use two 5 x 5 x 3 filters instead of one. Then our output volume would be 28 x 28 x 2. By using more filters, we are able to preserve the spatial dimensions better. Mathematically, this is whats going on in a convolutional layer.

However, lets talk about what this convolution is actually doing from a high level. Each of these filters can be thought of as feature identifiers. When I say features, Im talking about things like straight edges, simple colors, and curves. Think about the simplest characteristics that all images have in common with each other. Lets say our first filter is 7 x 7 x 3 and is going to be a curve detector. (In this section, lets ignore the fact that the filter is 3 units deep and only consider the top depth slice of the filter and the image, for simplicity.)As a curve detector, the filter will have a pixel structure in which there will be higher numerical values along the area that is a shape of a curve (Remember, these filters that were talking about as just numbers!).

Now, lets go back to visualizing this mathematically. When we have this filter at the top left corner of the input volume, it is computing dot products between the filter and pixel values at that region. Now lets take an example of an image that we want to classify, and lets put our filter at the top left corner.

Basically, in the input image, if there is a shape that generally resembles the curve that this filter is representing, then all of the dot products summed together will result in a large value! Now lets see what happens when we move our filter.

The value is much lower! This is because there wasnt anything in the image section that responded to the curve detector filter. Remember, the output of this conv layer is an activation map. So, in the simple case of a one filter convolution (and if that filter is a curve detector), the activation map will show the areas in which there at mostly likely to be curves in the picture. In this example, the top left value of our 28 x 28 x 1 activation map will be 6600. This high value means that it is likely that there is some sort of curve in the input volume that caused the filter to activate. The top right value in our activation map will be 0 because there wasnt anything in the input volume that caused the filter to activate (or more simply said, there wasnt a curve in that region of the original image). Remember, this is just for one filter. This is just a filter that is going to detect lines that curve outward and to the right. We can have other filters for lines that curve to the left or for straight edges. The more filters, the greater the depth of the activation map, and the more information we have about the input volume.

The first convolutional layer filters the 2242243 input image with 96 kernels of size 11113 with a stride of 4 pixels (this is the distance between the receptive field centers of neighboring neurons in a kernel map).

Figure 2: An illustration of the architecture of our CNN, explicitly showing the delineation of responsibilities between the two GPUs. One GPU runs the layer-parts at the top of the figure while the other runs the layer-parts at the bottom. The GPUs communicate only at certain layers. The networks input is 150,528-dimensional, and the number of neurons in the networks remaining layers is given by 253,440186,62464,89664,89643,264 409640961000. neurons in a kernel map).

The second convolutional layer takes as input the (response-normalized and pooled) output of the first convolutional layer and filters it with 256 kernels of size 5 5 48. The third, fourth, and fifth convolutional layers are connected to one another without any intervening pooling or normalization layers. The third convolutional layer has 384 kernels of size 3 3 256 connected to the (normalized, pooled) outputs of the second convolutional layer. The fourth convolutional layer has 384 kernels of size 3 3 192 , and the fifth convolutional layer has 256 kernels of size 3 3 192. The fully-connected layers have 4096 neurons each.

The process of forward pass, loss function, backward pass, and parameter update is generally called one epoch. The program will repeat this process for a fixed number of epochs for each training image.

gx-f advanced fiber laser - artificial intelligence

gx-f advanced fiber laser - artificial intelligence

Power lies in what a fiber laser can do, not the kilowatts it has. With the manufacturing industry suffering from a shortage of experienced workers, Mitsubishi designed this new generation of fiber lasers to minimize the need for operator input while maximizing quality and productivity.

machine input output - solved examples

machine input output - solved examples

In the reasoning section, one of the important topics is MachineInput Output problems. Here you can check some of the important types of Machine Input Output problems. You can also check the examples of some important problems which are asked in various bank exams however, we cant expect the same pattern in the upcoming exams.

Input : day 74 night 36 25 68 all for Step 1 : all day 74 night 36 25 68 for Step 2 : all 74 day night 36 25 68 for Step 3 : all 74 day 68 night 36 25 for Step 4 : all 74 day 68 for night 36 25 Step 5 : all 74 day 68 for 36 night 25 Step 5 is the last step of the rearrangement of the input.

Look at the last step of the input, words are arranged in alphabetical order and the numbers are arranged in descending order. In all the steps only one number/word is shifted. Shifting is performed fro left to right only i.e Single Side Shifting.

Input: games 79 go glacier 57 14 give 86 63 gender 42 get Step I: glacier games 79 go 57 give 86 63 gender 42 get 41 Step II: gender glacier games 79 go 57 give 86 63 get 41 24 Step III: games gender glacier 79 go give 86 63 get 41 24 75 Step IV: give games gender glacier 79 go 86 get 41 go 75 36 Step V: get give games gender glacier go 86 41 24 75 36 97 Step VI: go get give games gender glacier 41 24 75 36 97 68 Step VI is the last step of the rearrangement of the input.

In this type, look at the final arrangement the words are shifted as per the total number of letters. For Example, go two letter word; get three letter word and so on. Numbers are arranged in ascending order as per the input (but the digits are reversed while shifting. For Example 14 41, 42-24). In all the steps, both word and number are arranged in both ends of the row.

Input: 41 sprain 10 early 97 noble 26 65 ankle death Step I: 97 41 10 early noble 26 65 ankle death sprain Step II: noble 97 41 10 early 26 ankle death sprain 65 Step III: 41 noble 97 10 26 ankle sprain 65 early Step IV: death 41 noble 97 10 ankle sprain 65 early 26 Step V: 10 death 41 noble 97 sprain 65 early 26 ankle

Input: any number less than 30 and more than 20 does not equal 40 Step I: than 20 any number less than 30 and more does not equal 40 Step II: than 20 than 30 any number less and more does not equal 40 Step III: than 20 than 30 equal 40 any number less and more does not Step IV: than 20 than 30 equal 40 number any less and more does not Step V: than 20 than 30 equal 40 number not any less and more does Step VI: than 20 than 30 equal 40 number not more any less and does Step VII: than 20 than 30 equal 40 number not more less any and does Step VIII: than 20 than 30 equal 40 number not more less does any

Input: Apple Ball Cat Doll Egg Fan Gun Step 1: Gun Cat Ball Doll Egg Fan Apple Step 2: Cat Gun Doll Ball Egg Apple Fan Step 3: Fan Doll Gun Ball Egg Apple Cat Step 4: Doll Fan Ball Gun Egg Cat Apple Pattern Explanation: Apple 1; Ball 2; Cat 3 and so on Step 1: 7 3 2 4 5 6 1 Step 2: 3 7 4 2 5 1 6 Step 3: 6 4 7 2 5 1 3 Step 4: 4 6 2 7 5 3 1

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