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: 31 20 52 58 54 14. After step 2, 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: 54 80 72 65 10 13. After step 4, 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: 41 49 18 83 56 58. After step 4, what is the 2nd number from the left?
- 4.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?
- 5.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?
- 6.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?
- 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: 29 35 23 10 64 18. After step 3, what is the 5th number from the left?
- 8.A number machine multiplies a number by 2 and then takes away 2. Each output goes back in as the next input. Start with 6. What comes out after step 3?
- 9.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: 14 58 78 89 46 73. After step 2, what is the 6th number from the left?
- 10.A number machine multiplies a number by 2 and then adds 4. Each output goes back in as the next input. Start with 3. What comes out after step 3?
- 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: 62 82 63 21 42 79. After step 2, what is the 6th 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: 19 75 15 98 83 96. After step 3, what is the 2nd number from the left?
- 13.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 21 60 51 64 45. After step 3, 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: 53 79 94 82 38 35. After step 4, what is the 4th 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: 72 64 52 14 95 28. After step 3, 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: 45 88 16 89 95 56. After step 4, what is the 6th number from the left?
- 17.A number machine multiplies a number by 2 and then takes away 3. Each output goes back in as the next input. Start with 4. 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: 16 30 49 44 51 62. After step 3, what is the 2nd 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: 70 81 17 28 97 25. After step 3, what is the 4th number from the left?
- 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: 18 98 22 41 17 40. After step 4, what is the 1st 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: 72 43 14 53 84 41. After step 2, what is the 3rd 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: 98 62 96 33 52 32. After step 4, what is the 1st number from the left?
- 23.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 38 20 74 68 27. After step 2, what is the 4th number from the left?
- 24.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 2?
- 25.A number machine multiplies a number by 3 and then takes away 4. Each output goes back in as the next input. Start with 5. What comes out after step 3?
- 26.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?
- 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: 19 42 56 73 96 50. After step 3, what is the 5th number from the left?
- 28.A number machine multiplies a number by 2 and then adds 1. Each output goes back in as the next input. Start with 4. What comes out after step 2?
- 29.A number machine multiplies a number by 2 and then adds 2. Each output goes back in as the next input. Start with 5. What comes out after step 3?
- 30.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 51 48 81 92 14. After step 2, what is the 1st number from the left?
- 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: 38 66 95 39 70 15. After step 2, what is the 3rd number from the left?
- 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: 95 67 64 43 60 26. After step 4, what is the 2nd 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: 10 96 21 56 54 99. After step 4, what is the 6th number from the left?
- 34.A number machine multiplies a number by 3 and then takes away 1. Each output goes back in as the next input. Start with 7. What comes out after step 3?
- 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: 44 26 73 16 59 91. 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: 45 86 83 67 11 65. After step 3, what is the 6th 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: 61 51 20 23 66 79. After step 3, what is the 4th number from the left?
- 38.A number machine multiplies a number by 3 and then takes away 1. Each output goes back in as the next input. Start with 6. What comes out after step 3?
- 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: 32 67 77 46 79 24. After step 3, what is the 5th 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: 62 85 37 13 88 30. After step 3, what is the 6th number from the left?
Answer key
- 31
- 13
- 58
- 88
- 89
- 13
- 35
- 34
- 73
- 52
- 42
- 19
- 51
- 53
- 95
- 16
- 11
- 30
- 17
- 98
- 72
- 98
- 38
- 39
- 83
- 27
- 73
- 19
- 54
- 14
- 66
- 67
- 99
- 176
- 44
- 67
- 61
- 149
- 46
- 30
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