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 biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 21 61 83 82 58 66. After step 3, what is the 2nd 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: 82 94 59 10 63 93. After step 2, what is the 2nd number from the left?
- 3.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: 43 35 93 92 80 66. After step 3, what is the 5th number from the left?
- 4.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?
- 5.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: 21 51 20 16 78 93. After step 2, what is the 1st number from the left?
- 6.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: 79 32 89 66 40 77. After step 3, what is the 5th 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: 99 17 73 34 46 40. After step 2, what is the 6th 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: 90 31 43 21 49 54. After step 4, what is the 6th number from the left?
- 9.A number machine multiplies a number by 3 and then takes away 1. Each output goes back in as the next input. Start with 8. What comes out after step 3?
- 10.A number machine multiplies a number by 3 and then adds 4. Each output goes back in as the next input. Start with 2. 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: 34 83 13 81 89 53. After step 3, what is the 1st number from the left?
- 12.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: 27 41 86 96 17 64. After step 3, what is the 3rd number from the left?
- 13.A number machine multiplies a number by 3 and then adds 1. Each output goes back in as the next input. Start with 3. What comes out after step 2?
- 14.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?
- 15.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: 46 97 68 16 26 70. After step 2, what is the 1st 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: 71 76 66 10 36 14. After step 2, what is the 3rd number from the left?
- 17.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?
- 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: 87 20 61 79 31 26. After step 2, what is the 6th number from the left?
- 19.A number machine multiplies a number by 2 and then adds 5. Each output goes back in as the next input. Start with 3. What comes out after step 2?
- 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: 28 43 93 78 13 74. After step 3, what is the 4th 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: 25 38 19 35 36 22. After step 2, what is the 1st number from the left?
- 22.A number machine multiplies a number by 3 and then adds 5. Each output goes back in as the next input. Start with 3. What comes out after step 3?
- 23.A number machine multiplies a number by 2 and then adds 3. Each output goes back in as the next input. Start with 6. What comes out after step 2?
- 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: 93 90 40 45 72 41. After step 2, what is the 3rd number from the left?
- 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: 27 84 73 86 26 34. After step 3, what is the 2nd 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: 95 62 26 44 93 40. After step 4, what is the 4th number from the left?
- 27.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 96 99 95 38 14. After step 3, what is the 1st number from the left?
- 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: 93 85 70 94 64 37. After step 2, what is the 5th number from the left?
- 29.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 16 89 37 13 81. After step 2, what is the 2nd number from the left?
- 30.A number machine multiplies a number by 2 and then adds 3. Each output goes back in as the next input. Start with 4. What comes out after step 3?
- 31.A number machine multiplies a number by 3 and then adds 2. Each output goes back in as the next input. Start with 3. What comes out after step 3?
- 32.A number machine multiplies a number by 3 and then adds 3. Each output goes back in as the next input. Start with 3. What comes out after step 3?
- 33.A number machine multiplies a number by 3 and then takes away 1. Each output goes back in as the next input. Start with 5. What comes out after step 2?
- 34.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: 49 83 57 17 84 81. After step 4, what is the 4th number from the left?
- 35.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: 36 11 15 52 32 92. After step 3, what is the 3rd 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: 30 83 19 36 49 24. After step 3, what is the 2nd 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: 91 75 31 78 72 61. After step 2, what is the 2nd 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: 12 62 42 36 65 92. After step 2, what is the 1st number from the left?
- 39.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: 29 32 28 34 62 93. After step 2, what is the 3rd number from the left?
- 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: 21 90 33 41 76 44. After step 2, what is the 2nd number from the left?
Answer key
- 82
- 59
- 35
- 26
- 93
- 66
- 40
- 21
- 203
- 34
- 13
- 64
- 31
- 89
- 97
- 66
- 107
- 31
- 27
- 28
- 19
- 146
- 33
- 93
- 84
- 44
- 14
- 70
- 81
- 53
- 107
- 120
- 41
- 57
- 36
- 24
- 61
- 12
- 29
- 76
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