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: 72 11 29 81 97 65. After step 2, what is the 1st number from the left?
- 2.A number machine multiplies a number by 2 and then takes away 1. Each output goes back in as the next input. Start with 2. What comes out after step 3?
- 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: 88 64 17 83 89 48. After step 2, what is the 4th number from the left?
- 4.A number machine multiplies a number by 3 and then takes away 4. Each output goes back in as the next input. Start with 9. What comes out after step 2?
- 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: 67 19 21 88 35 38. After step 3, what is the 5th 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: 70 67 21 31 40 63. After step 4, what is the 4th 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: 99 32 91 50 81 95. 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: 20 77 26 43 70 72. After step 2, what is the 2nd 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: 69 29 28 13 79 71. After step 2, what is the 1st number from the left?
- 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: 67 54 19 24 80 32. After step 2, what is the 4th number from the left?
- 11.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 68 52 17 82 75. After step 3, what is the 3rd 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: 56 36 77 51 75 89. After step 3, what is the 3rd number from the left?
- 13.A number machine multiplies a number by 3 and then adds 3. Each output goes back in as the next input. Start with 4. What comes out after step 3?
- 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: 32 99 78 37 77 88. 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 biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 35 60 55 27 36 53. 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 smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 34 62 32 85 68 78. After step 4, what is the 4th number from the left?
- 17.A number machine multiplies a number by 2 and then takes away 4. Each output goes back in as the next input. Start with 5. What comes out after step 2?
- 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: 77 39 12 47 82 88. After step 2, what is the 1st number from the left?
- 19.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: 19 16 46 11 32 14. After step 2, what is the 2nd number from the left?
- 20.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 2?
- 21.A number machine multiplies a number by 2 and then adds 3. Each output goes back in as the next input. Start with 7. What comes out after step 2?
- 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: 27 83 85 79 14 80. After step 4, what is the 4th 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: 72 66 16 58 88 69. After step 2, what is the 6th number from the left?
- 24.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 14 46 53 26 19. After step 2, what is the 2nd 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: 80 78 60 20 71 70. After step 3, what is the 2nd number from the left?
- 26.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 2?
- 27.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: 68 28 86 75 71 38. After step 2, what is the 4th number from the left?
- 28.A number machine multiplies a number by 2 and then takes away 5. Each output goes back in as the next input. Start with 6. What comes out after step 3?
- 29.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: 88 62 81 27 84 99. After step 3, what is the 1st number from the left?
- 30.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?
- 31.A number machine multiplies a number by 2 and then adds 2. Each output goes back in as the next input. Start with 6. What comes out after step 2?
- 32.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: 31 13 47 99 79 33. After step 4, what is the 3rd number from the left?
- 33.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: 44 97 43 94 78 67. After step 2, what is the 1st number from the left?
- 34.A number machine multiplies a number by 2 and then adds 4. Each output goes back in as the next input. Start with 4. What comes out after step 2?
- 35.A number machine multiplies a number by 3 and then adds 1. Each output goes back in as the next input. Start with 4. What comes out after step 3?
- 36.A number machine multiplies a number by 2 and then takes away 2. Each output goes back in as the next input. Start with 3. What comes out after step 3?
- 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: 64 72 40 18 31 33. After step 4, what is the 4th number from the left?
- 38.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: 76 27 61 47 21 38. After step 3, what is the 1st 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 5. 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: 55 36 87 35 47 45. After step 3, what is the 2nd number from the left?
Answer key
- 97
- 9
- 17
- 65
- 21
- 40
- 81
- 72
- 79
- 19
- 75
- 56
- 147
- 77
- 60
- 68
- 8
- 88
- 32
- 35
- 37
- 79
- 69
- 53
- 60
- 26
- 28
- 13
- 27
- 31
- 30
- 47
- 43
- 28
- 121
- 10
- 40
- 76
- 109
- 55
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