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: 61 57 31 96 21 46. After step 2, what is the 1st number from the left?
- 2.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 61 27 14 93 46. After step 2, what is the 6th 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: 27 14 93 25 82 37. After step 4, what is the 5th number from the left?
- 4.A number machine multiplies a number by 3 and then adds 3. Each output goes back in as the next input. Start with 7. What comes out after step 3?
- 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: 73 88 57 75 15 61. After step 3, what is the 6th number from the left?
- 6.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 97 29 20 91 42. After step 3, what is the 6th 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: 20 62 50 80 84 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: 27 98 15 43 28 34. After step 2, what is the 3rd 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: 88 79 15 71 31 67. After step 2, what is the 5th number from the left?
- 10.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?
- 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: 50 35 31 21 81 23. After step 4, 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: 31 11 72 88 33 37. After step 3, what is the 5th number from the left?
- 13.A number machine multiplies a number by 2 and then takes away 3. Each output goes back in as the next input. Start with 5. What comes out after step 3?
- 14.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: 53 81 75 99 49 59. After step 2, what is the 4th 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: 36 75 91 52 45 83. After step 4, what is the 2nd 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: 42 12 16 57 67 71. After step 2, what is the 1st number from the left?
- 17.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?
- 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: 48 94 56 44 54 20. After step 2, what is the 6th 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: 98 75 49 13 43 58. After step 2, what is the 4th number from the left?
- 20.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?
- 21.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 2?
- 22.A number machine multiplies a number by 3 and then adds 2. Each output goes back in as the next input. Start with 4. 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: 11 26 38 37 83 58. After step 2, what is the 3rd number from the left?
- 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: 48 97 84 94 61 75. After step 2, what is the 4th number from the left?
- 25.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?
- 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: 12 54 65 44 77 43. After step 2, what is the 6th number from the left?
- 27.A number machine multiplies a number by 2 and then adds 4. Each output goes back in as the next input. Start with 5. What comes out after step 2?
- 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: 69 90 24 93 42 76. After step 2, what is the 2nd 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: 72 26 78 59 30 85. After step 2, what is the 1st number from the left?
- 30.A number machine multiplies a number by 3 and then takes away 3. Each output goes back in as the next input. Start with 7. What comes out after step 2?
- 31.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 50 37 22 25 98. After step 3, what is the 6th number from the left?
- 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: 65 80 21 44 88 73. After step 4, what is the 1st number from the left?
- 33.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: 11 23 17 32 61 80. After step 3, what is the 1st number from the left?
- 34.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: 49 44 45 98 97 25. After step 2, what is the 6th number from the left?
- 35.A number machine multiplies a number by 2 and then takes away 2. Each output goes back in as the next input. Start with 9. What comes out after step 2?
- 36.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 2?
- 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: 55 60 53 16 23 19. After step 3, what is the 1st 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: 67 23 57 62 41 95. After step 4, what is the 4th number from the left?
- 39.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: 37 59 28 18 44 35. After step 4, what is the 2nd 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: 87 60 71 13 48 20. After step 2, what is the 6th number from the left?
Answer key
- 96
- 46
- 93
- 228
- 75
- 42
- 80
- 27
- 31
- 26
- 31
- 11
- 19
- 75
- 45
- 12
- 5
- 54
- 13
- 27
- 68
- 44
- 38
- 84
- 10
- 43
- 32
- 90
- 85
- 51
- 25
- 21
- 80
- 97
- 30
- 22
- 60
- 62
- 28
- 20
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