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: 16 11 47 51 23 28. After step 4, what is the 1st 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: 57 14 21 22 34 35. After step 2, what is the 5th 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: 91 28 96 48 19 41. After step 4, what is the 3rd number from the left?
- 4.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 23 57 27 47 73. After step 4, what is the 5th number from the left?
- 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: 80 52 36 55 51 68. After step 2, what is the 4th 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: 24 74 62 87 44 93. After step 3, what is the 6th number from the left?
- 7.A number machine multiplies a number by 2 and then adds 2. Each output goes back in as the next input. Start with 8. What comes out after step 3?
- 8.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: 65 92 40 44 48 42. After step 3, what is the 4th number from the left?
- 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: 65 93 22 58 66 96. After step 2, what is the 3rd 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: 24 14 98 18 80 34. After step 3, what is the 2nd number from the left?
- 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: 83 62 61 29 37 36. After step 2, what is the 3rd 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: 19 23 72 27 38 49. After step 3, what is the 1st number from the left?
- 13.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?
- 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: 39 31 60 54 32 26. After step 4, what is the 2nd 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: 91 88 62 40 41 17. After step 4, what is the 6th 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: 12 73 48 37 35 31. After step 3, what is the 2nd 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 50 23 93 44 79. 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 smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 41 98 26 12 82 33. 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 smallest number not yet arranged and moves it to the left, just after the numbers already arranged; the others keep their order. Input: 29 68 15 25 60 32. After step 4, what is the 3rd 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: 31 28 24 14 80 23. After step 3, what is the 3rd number from the left?
- 21.A number machine multiplies a number by 2 and then adds 1. Each output goes back in as the next input. Start with 8. 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: 77 11 44 19 18 28. After step 4, what is the 3rd 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: 25 62 83 81 54 49. After step 2, 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: 60 77 22 23 36 65. After step 4, what is the 2nd number from the left?
- 25.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 2?
- 26.A number machine multiplies a number by 2 and then adds 1. Each output goes back in as the next input. Start with 5. 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: 82 76 86 21 98 43. After step 4, what is the 1st number from the left?
- 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: 39 73 95 14 50 38. After step 3, what is the 4th 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: 15 82 45 20 98 41. After step 3, what is the 5th 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 8. What comes out after step 2?
- 31.A number machine multiplies a number by 3 and then takes away 2. Each output goes back in as the next input. Start with 4. 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: 52 54 60 35 41 59. After step 3, what is the 5th number from the left?
- 33.A number machine multiplies a number by 3 and then adds 3. Each output goes back in as the next input. Start with 8. 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: 79 28 81 34 19 29. After step 3, what is the 3rd number from the left?
- 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 2?
- 36.A number machine multiplies a number by 3 and then takes away 2. Each output goes back in as the next input. Start with 4. What comes out after step 3?
- 37.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 81 14 24 36 54. After step 4, what is the 5th number from the left?
- 38.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?
- 39.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?
- 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: 59 53 17 40 38 20. After step 3, what is the 1st number from the left?
Answer key
- 11
- 34
- 41
- 23
- 52
- 44
- 78
- 65
- 65
- 80
- 83
- 72
- 46
- 54
- 17
- 48
- 93
- 12
- 29
- 28
- 35
- 28
- 83
- 65
- 29
- 23
- 98
- 39
- 45
- 41
- 28
- 60
- 84
- 34
- 40
- 82
- 14
- 67
- 10
- 17
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