Input Output Reasoning Worksheet
How to think it through (One step, one line): Read the rule carefully: what moves (or changes) in each step? Write the list (or number) after step 1, step 2, step 3 … each on a new line. Stop at the step asked and read the answer.
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- 1.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 33 19 20 17 32 61. After step 3, what is the 3rd number from the left?
- 2.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 36 45 33 21 49 52. After step 3, what is the 6th number from the left?
- 3.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 11 99 25 57 15 75. After step 3, what is the 6th number from the left?
- 4.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 22 61 27 70 87 60. After step 3, what is the 2nd number from the left?
- 5.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 73 98 76 45 17 33. After step 3, what is the 4th number from the left?
- 6.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 85 75 20 79 33 27. After step 4, what is the 5th number from the left?
- 7.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 30 90 64 72 33 80. After step 2, what is the 1st number from the left?
- 8.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 83 76 42 27 54 71. After step 4, what is the 3rd number from the left?
- 9.A number machine multiplies a number by 3 and then takes away 5. Each output goes back in as the next input. Start with 6. What comes out after step 2?
- 10.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 95 47 40 73 45 64. After step 3, what is the 4th number from the left?
- 11.A number machine multiplies a number by 3 and then takes away 2. Each output goes back in as the next input. Start with 7. What comes out after step 3?
- 12.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 29 84 27 57 75 94. After step 2, what is the 6th number from the left?
- 13.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 56 53 68 16 89 67. After step 4, what is the 5th number from the left?
- 14.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 48 91 32 47 18 67. After step 2, what is the 6th number from the left?
- 15.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 82 37 90 51 60 62. After step 2, what is the 3rd number from the left?
- 16.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 38 55 73 53 51 33. After step 2, what is the 6th number from the left?
- 17.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 67 44 66 43 68 87. After step 2, what is the 1st number from the left?
- 18.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 78 95 51 42 82 91. After step 3, what is the 4th number from the left?
- 19.A number machine multiplies a number by 3 and then adds 5. Each output goes back in as the next input. Start with 6. What comes out after step 3?
- 20.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 85 59 47 89 39 27. After step 4, what is the 3rd number from the left?
- 21.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 83 30 88 90 16 45. After step 3, what is the 6th number from the left?
- 22.A number machine multiplies a number by 2 and then adds 5. Each output goes back in as the next input. Start with 9. What comes out after step 3?
- 23.A number machine multiplies a number by 3 and then takes away 3. Each output goes back in as the next input. Start with 2. What comes out after step 3?
- 24.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 39 34 75 19 18 38. After step 3, what is the 1st number from the left?
- 25.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 25 77 99 68 71 64. After step 2, what is the 2nd number from the left?
- 26.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 46 88 90 74 81 66. After step 2, what is the 2nd number from the left?
- 27.A number machine multiplies a number by 3 and then takes away 1. Each output goes back in as the next input. Start with 4. What comes out after step 2?
- 28.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 29 21 37 85 87 31. After step 2, what is the 1st number from the left?
- 29.A number machine multiplies a number by 2 and then adds 1. Each output goes back in as the next input. Start with 5. What comes out after step 2?
- 30.A number machine multiplies a number by 3 and then adds 4. Each output goes back in as the next input. Start with 6. What comes out after step 3?
- 31.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 31 80 56 50 93 76. After step 4, what is the 2nd number from the left?
- 32.A number machine multiplies a number by 2 and then takes away 2. Each output goes back in as the next input. Start with 5. What comes out after step 3?
- 33.A machine arranges numbers step by step. In each step it takes the biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 78 19 18 97 88 75. After step 4, what is the 3rd number from the left?
- 34.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 73 42 98 43 27 18. After step 2, what is the 6th number from the left?
- 35.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 59 52 39 36 76 92. After step 2, what is the 4th number from the left?
- 36.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 91 23 25 45 50 35. After step 4, what is the 4th number from the left?
- 37.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 56 38 71 45 88 32. After step 3, what is the 4th number from the left?
- 38.A machine arranges numbers step by step. In each step it takes the smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 67 87 85 24 11 27. After step 3, what is the 1st number from the left?
- 39.A number machine multiplies a number by 3 and then takes away 5. Each output goes back in as the next input. Start with 4. What comes out after step 2?
- 40.A number machine multiplies a number by 3 and then adds 1. Each output goes back in as the next input. Start with 2. What comes out after step 3?
Answer key
- 20
- 52
- 75
- 27
- 73
- 85
- 90
- 54
- 34
- 47
- 163
- 94
- 68
- 18
- 82
- 33
- 43
- 78
- 227
- 59
- 90
- 107
- 15
- 18
- 64
- 66
- 32
- 21
- 23
- 214
- 50
- 26
- 78
- 43
- 52
- 45
- 56
- 11
- 16
- 67
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