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: 43 32 51 88 63 38. After step 4, what is the 4th 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: 66 26 18 46 70 92. After step 3, what is the 3rd 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: 80 48 53 41 44 36. After step 3, what is the 2nd number from the left?
- 4.A number machine multiplies a number by 3 and then takes away 2. Each output goes back in as the next input. Start with 6. What comes out after step 2?
- 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: 98 31 94 46 77 55. After step 4, what is the 6th 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: 31 81 36 86 55 49. After step 3, what is the 2nd number from the left?
- 7.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: 45 20 16 33 37 66. After step 4, what is the 5th number from the left?
- 8.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: 87 42 14 40 16 24. After step 2, what is the 6th number from the left?
- 9.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: 98 28 87 27 64 57. After step 4, what is the 1st number from the left?
- 10.A number machine multiplies a number by 3 and then adds 4. Each output goes back in as the next input. Start with 8. What comes out after step 2?
- 11.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: 40 25 77 72 89 29. After step 2, what is the 2nd number from the left?
- 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: 52 39 45 11 56 44. After step 4, 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: 82 28 40 66 43 60. After step 3, what is the 1st number from the left?
- 14.A number machine multiplies a number by 2 and then adds 2. Each output goes back in as the next input. Start with 4. What comes out after step 3?
- 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: 56 87 45 91 61 21. After step 3, what is the 2nd 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: 45 18 78 31 15 76. After step 4, what is the 6th number from the left?
- 17.A number machine multiplies a number by 3 and then adds 2. Each output goes back in as the next input. Start with 2. What comes out after step 3?
- 18.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: 24 26 10 28 71 97. After step 2, what is the 6th number from the left?
- 19.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 30 61 89 36 42. After step 2, what is the 3rd number from the left?
- 20.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: 95 34 20 83 46 74. After step 3, what is the 2nd 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: 24 43 17 16 31 61. After step 2, what is the 6th number from the left?
- 22.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: 71 33 73 42 84 32. After step 2, what is the 2nd number from the left?
- 23.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: 41 64 35 56 20 69. After step 3, what is the 6th number from the left?
- 24.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 2?
- 25.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: 89 18 68 27 23 42. After step 2, what is the 1st number from the left?
- 26.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: 81 31 44 15 63 23. After step 4, what is the 4th number from the left?
- 27.A number machine multiplies a number by 3 and then adds 4. Each output goes back in as the next input. Start with 4. What comes out after step 3?
- 28.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: 28 34 38 14 52 88. After step 4, what is the 4th number from the left?
- 29.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?
- 30.A number machine multiplies a number by 2 and then adds 1. Each output goes back in as the next input. Start with 6. What comes out after step 2?
- 31.A number machine multiplies a number by 3 and then adds 2. Each output goes back in as the next input. Start with 9. What comes out after step 2?
- 32.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 10 30 91 80 67. After step 2, what is the 1st number from the left?
- 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: 40 72 82 81 15 85. After step 3, what is the 5th 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: 74 83 92 69 25 37. After step 2, what is the 2nd number from the left?
- 35.A number machine multiplies a number by 3 and then takes away 4. Each output goes back in as the next input. Start with 7. What comes out after step 2?
- 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: 31 32 81 26 90 60. After step 2, what is the 3rd number from the left?
- 37.A number machine multiplies a number by 2 and then takes away 1. Each output goes back in as the next input. Start with 9. What comes out after step 2?
- 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: 23 15 69 10 31 14. After step 4, what is the 5th number from the left?
- 39.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?
- 40.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 66 74 59 70 53. After step 4, what is the 4th number from the left?
Answer key
- 51
- 46
- 41
- 46
- 94
- 36
- 45
- 24
- 98
- 88
- 29
- 56
- 28
- 46
- 45
- 15
- 80
- 97
- 61
- 34
- 61
- 73
- 69
- 6
- 89
- 31
- 160
- 34
- 67
- 27
- 89
- 10
- 72
- 37
- 47
- 32
- 33
- 69
- 163
- 66
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