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: 23 33 89 22 68 18. After step 2, what is the 4th 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 8. What comes out after step 3?
- 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: 92 61 29 27 19 21. After step 4, what is the 4th 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: 23 83 76 20 79 51. After step 4, what is the 1st number from the left?
- 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: 30 89 16 21 78 69. After step 2, what is the 2nd 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: 33 68 18 51 25 91. After step 3, what is the 1st number from the left?
- 7.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?
- 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: 47 35 43 77 39 67. After step 4, what is the 6th number from the left?
- 9.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 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: 65 95 20 63 28 26. After step 2, what is the 1st number from the left?
- 11.A number machine multiplies a number by 3 and then adds 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 biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 59 43 50 86 19 35. After step 4, what is the 4th 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: 34 86 72 16 23 25. After step 3, what is the 1st 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 88 27 96 40 22. After step 3, what is the 1st 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: 74 73 68 32 10 69. After step 2, what is the 4th 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: 24 10 89 43 19 55. 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 biggest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 81 29 80 37 69 93. After step 4, 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: 75 53 45 21 63 46. After step 2, what is the 3rd 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: 68 91 59 55 98 34. After step 2, what is the 6th number from the left?
- 20.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?
- 21.A number machine multiplies a number by 2 and then adds 1. Each output goes back in as the next input. Start with 7. What comes out after step 3?
- 22.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 2?
- 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: 68 98 11 12 38 73. After step 4, what is the 4th 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: 92 65 99 94 33 70. After step 3, what is the 6th 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: 65 53 75 52 30 43. After step 3, what is the 1st 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: 29 87 94 11 64 31. After step 2, what is the 3rd 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 7. 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: 66 24 96 42 16 28. After step 2, what is the 3rd number from the left?
- 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: 66 63 76 18 84 22. After step 4, what is the 4th number from the left?
- 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 8. 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: 60 43 17 46 95 70. After step 3, what is the 3rd number from the left?
- 33.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?
- 34.A number machine multiplies a number by 2 and then adds 1. Each output goes back in as the next input. Start with 9. What comes out after step 2?
- 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: 86 70 81 72 69 34. After step 3, what is the 1st number from the left?
- 36.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 15 83 32 34 72. After step 3, what is the 1st number from the left?
- 37.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 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: 39 24 47 88 16 17. After step 4, what is the 2nd 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: 10 93 82 86 24 95. After step 2, what is the 1st number from the left?
- 40.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 22 27 39 68 79. After step 3, what is the 1st number from the left?
Answer key
- 33
- 57
- 29
- 20
- 78
- 91
- 31
- 39
- 7
- 95
- 215
- 43
- 86
- 96
- 73
- 55
- 93
- 53
- 98
- 47
- 63
- 5
- 68
- 70
- 75
- 87
- 241
- 24
- 66
- 27
- 80
- 46
- 15
- 39
- 86
- 83
- 9
- 17
- 95
- 14
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