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Input output reasoning questions with answers

Input output reasoning questions show a machine rearranging a line of words and numbers one step at a time, and ask for a later step or the step count. The entire skill is deducing the rule from two consecutive steps and then applying it mechanically. Each walkthrough below prints every intermediate step, which is what makes the rule visible rather than merely stated.

Download the PDF — 12 questions with answers

Free, ungated, no email. This is the input output reasoning questions with answers PDF — the same 12 questions as below, with every worked solution at the back, ready to print.

How to use this set

The 12 questions below are ordered the way an exam block is rather than easiest-first: two gentle openers, then a run of medium, and a hard one every sixth question — 2 of the 12 sit in the hard band. Every question is a input-output (machine rearrangement).

Work each question on paper before you open its solution. The walkthrough is the method itself, step for step, so reading it first turns a practice set into a reading exercise and teaches nothing. If you are stuck on the method rather than on one question, the method guide is a better place to start than the next question: All reasoning topics, with the method for each.

12 input output reasoning questions with answers

Every question below was generated by the same engine that mints the DeducePuzzles daily puzzle round, and machine-checked before it reached this page — a multiple-choice question validates its own answer against its own options at generation, and ships only with a walkthrough attached. The walkthrough is the engine's own.

Question 1

A machine rearranges an input line of words and numbers step by step, following one fixed rule (study the sample below). What is Step II for the New Input?

Sample Input: 19 piano island 79 24

Step I: 19 24 piano island 79

Step II: 19 24 79 piano island

Step II is the last step of the sample.

New Input: candle 66 72 house 29

  1. 66 72 29 house candle
  2. 66 72 29 candle house
  3. candle house 29 66 72
  4. 29 66 candle 72 house
  5. 72 66 candle house 29
Show the worked solution
  1. The machine's rule: in each step the machine moves the smallest remaining number to the leftmost free position.
  2. Check the rule against the sample — it reproduces every shown step, and no other standard rearrangement rule does.
  3. Apply it to the new input: candle 66 72 house 29.
  4. Step I: 29 candle 66 72 house
  5. Step II: 29 66 candle 72 house
  6. So Step II of the new input is: 29 66 candle 72 house.

Question 2

A machine rearranges an input line of words and numbers step by step, following one fixed rule (study the sample below). How many steps does the machine need to complete the arrangement of the New Input?

Sample Input: iron zebra 67 37 66

Step I: 37 iron zebra 67 66

Step II: 37 66 iron zebra 67

Step III: 37 66 67 iron zebra

Step III is the last step of the sample.

New Input: river 43 pearl 88 18

  1. 5
  2. 1
  3. 2
  4. 4
  5. 3
Show the worked solution
  1. The machine's rule: in each step the machine moves the smallest remaining number to the leftmost free position.
  2. Check the rule against the sample — it reproduces every shown step, and no other standard rearrangement rule does.
  3. Apply it to the new input: river 43 pearl 88 18.
  4. Step I: 18 river 43 pearl 88
  5. Step II: 18 43 river pearl 88
  6. Step III: 18 43 88 river pearl
  7. The arrangement is complete after Step III, so the machine needs 3 steps.

Question 3

A machine applies one fixed arithmetic operation to every number at each step (study the sample below). What is Step II for the New Input?

Sample Input: 99 18 55 54 34

Step I: 396 72 220 216 136

Step II: 403 79 227 223 143

Step III: 7 16 11 7 8

Step III is the last step of the sample.

New Input: 21 53 87 46 82

  1. 84 212 348 184 328
  2. 10 12 13 11 11
  3. 91 219 355 191 335
  4. 73 201 337 173 317
  5. 32 4 96 32 48
Show the worked solution
  1. Sample Step I: each number is multiplied by 4 (99 → 396).
  2. Sample Step II: 7 is added to each number (396 → 403).
  3. Sample Step III: each number is replaced by the sum of its digits (403 → 7).
  4. Each of those is the only standard operation that turns the previous line into the shown one.
  5. Apply the same steps to the new input: 21 53 87 46 82.
  6. Step I: 84 212 348 184 328
  7. Step II: 91 219 355 191 335
  8. So Step II of the new input is: 91 219 355 191 335.

Question 4

A machine rearranges an input line of words and numbers step by step, following one fixed rule (study the sample below). What is Step II for the New Input?

Sample Input: 74 86 flute mango rock 21

Step I: rock 74 86 flute mango 21

Step II: rock flute 74 86 mango 21

Step III: rock flute mango 74 86 21

Step III is the last step of the sample.

New Input: 10 apple 58 47 engine orbit

  1. apple orbit 10 58 47 engine
  2. apple engine 10 58 47 orbit
  3. apple engine 10 orbit 47 58
  4. orbit engine 10 apple 58 47
  5. 10 apple engine orbit 47 58
Show the worked solution
  1. The machine's rule: in each step the machine moves the shortest remaining word (alphabetical order breaks a length tie) to the leftmost free position.
  2. Check the rule against the sample — it reproduces every shown step, and no other standard rearrangement rule does.
  3. Apply it to the new input: 10 apple 58 47 engine orbit.
  4. Step I: apple 10 58 47 engine orbit
  5. Step II: apple orbit 10 58 47 engine
  6. So Step II of the new input is: apple orbit 10 58 47 engine.

Question 5

A machine rearranges an input line of words and numbers step by step, following one fixed rule (study the sample below). What is Step II for the New Input?

Sample Input: 70 yard mirror rock 18 28

Step I: rock 70 yard mirror 18 28

Step II: rock yard 70 mirror 18 28

Step III: rock yard mirror 70 18 28

Step III is the last step of the sample.

New Input: 43 cloud 35 house kite 48

  1. 35 43 48 cloud house kite
  2. cloud house 35 kite 43 48
  3. cloud house kite 35 43 48
  4. cloud 35 43 house kite 48
  5. kite cloud 43 35 house 48
Show the worked solution
  1. The machine's rule: in each step the machine moves the shortest remaining word (alphabetical order breaks a length tie) to the leftmost free position.
  2. Check the rule against the sample — it reproduces every shown step, and no other standard rearrangement rule does.
  3. Apply it to the new input: 43 cloud 35 house kite 48.
  4. Step I: kite 43 cloud 35 house 48
  5. Step II: kite cloud 43 35 house 48
  6. So Step II of the new input is: kite cloud 43 35 house 48.

Question 6

A machine rearranges an input line of words and numbers step by step, following one fixed rule (study the sample below). How many steps does the machine need to complete the arrangement of the New Input?

Sample Input: 12 80 91 mango 20 bridge cloud lotus

Step I: cloud 12 80 91 mango 20 bridge lotus

Step II: cloud lotus 12 80 91 mango 20 bridge

(Only the first 2 steps of the sample are shown; the machine continues until the arrangement is complete.)

New Input: 95 yard 99 48 33 house river quilt

  1. 6
  2. 3
  3. 5
  4. 2
  5. 4
Show the worked solution
  1. The machine's rule: in each step the machine moves the shortest remaining word (alphabetical order breaks a length tie) to the leftmost free position.
  2. Check the rule against the sample — it reproduces every shown step, and no other standard rearrangement rule does.
  3. Apply it to the new input: 95 yard 99 48 33 house river quilt.
  4. Step I: yard 95 99 48 33 house river quilt
  5. Step II: yard house 95 99 48 33 river quilt
  6. Step III: yard house quilt 95 99 48 33 river
  7. Step IV: yard house quilt river 95 99 48 33
  8. The arrangement is complete after Step IV, so the machine needs 4 steps.

Question 7

A machine rearranges an input line of words and numbers step by step, following one fixed rule (study the sample below). What is Step II for the New Input?

Sample Input: pearl wagon 15 candle 41

Step I: pearl 15 candle 41 wagon

Step II: 15 candle 41 pearl wagon

Step III: 15 41 candle pearl wagon

Step III is the last step of the sample.

New Input: apple 13 ocean bridge 49

  1. apple 13 49 bridge ocean
  2. apple 13 bridge 49 ocean
  3. apple ocean bridge 13 49
  4. 49 13 apple ocean bridge
  5. 13 49 apple ocean bridge
Show the worked solution
  1. The machine's rule: in each step the machine moves the alphabetically last remaining word to the rightmost free position.
  2. Check the rule against the sample — it reproduces every shown step, and no other standard rearrangement rule does.
  3. Apply it to the new input: apple 13 ocean bridge 49.
  4. Step I: apple 13 bridge 49 ocean
  5. Step II: apple 13 49 bridge ocean
  6. So Step II of the new input is: apple 13 49 bridge ocean.

Question 8

A machine rearranges an input line of words and numbers step by step, following one fixed rule (study the sample below). What is Step II for the New Input?

Sample Input: 56 cloud 63 57 island

Step I: 56 cloud 57 island 63

Step II: 56 cloud island 57 63

Step III: cloud island 56 57 63

Step III is the last step of the sample.

New Input: 79 13 jam 48 candle

  1. 13 jam candle 48 79
  2. candle 13 79 jam 48
  3. 13 candle 79 jam 48
  4. jam candle 79 13 48
  5. candle jam 79 13 48
Show the worked solution
  1. The machine's rule: in each step the machine moves the largest remaining number to the rightmost free position.
  2. Check the rule against the sample — it reproduces every shown step, and no other standard rearrangement rule does.
  3. Apply it to the new input: 79 13 jam 48 candle.
  4. Step I: 13 jam 48 candle 79
  5. Step II: 13 jam candle 48 79
  6. So Step II of the new input is: 13 jam candle 48 79.

Question 9

A machine rearranges an input line of words and numbers step by step, following one fixed rule (study the sample below). What is Step III for the New Input?

Sample Input: 60 hill 81 jungle 83 ocean

Step I: hill 60 81 jungle 83 ocean

Step II: hill ocean 60 81 jungle 83

Step III: hill ocean jungle 60 81 83

Step III is the last step of the sample.

New Input: 39 bridge 86 mango queen 98

  1. queen mango bridge 39 86 98
  2. 39 86 98 bridge mango queen
  3. mango queen bridge 39 86 98
  4. 39 86 98 queen mango bridge
  5. bridge mango queen 39 86 98
Show the worked solution
  1. The machine's rule: in each step the machine moves the shortest remaining word (alphabetical order breaks a length tie) to the leftmost free position.
  2. Check the rule against the sample — it reproduces every shown step, and no other standard rearrangement rule does.
  3. Apply it to the new input: 39 bridge 86 mango queen 98.
  4. Step I: mango 39 bridge 86 queen 98
  5. Step II: mango queen 39 bridge 86 98
  6. Step III: mango queen bridge 39 86 98
  7. So Step III of the new input is: mango queen bridge 39 86 98.

Question 10

A machine applies one fixed arithmetic operation to every number at each step (study the sample below). What is Step III for the New Input?

Sample Input: 49 25 47 36 67

Step I: 98 50 94 72 134

Step II: 102 54 98 76 138

Step III: 96 48 92 70 132

Step III is the last step of the sample.

New Input: 69 76 89 23 43

  1. 568 624 728 200 360
  2. 142 156 182 50 90
  3. 148 162 188 56 96
  4. 136 150 176 44 84
  5. 136 150 176 44 74
Show the worked solution
  1. Sample Step I: each number is multiplied by 2 (49 → 98).
  2. Sample Step II: 4 is added to each number (98 → 102).
  3. Sample Step III: 6 is subtracted from each number (102 → 96).
  4. Each of those is the only standard operation that turns the previous line into the shown one.
  5. Apply the same steps to the new input: 69 76 89 23 43.
  6. Step I: 138 152 178 46 86
  7. Step II: 142 156 182 50 90
  8. Step III: 136 150 176 44 84
  9. So Step III of the new input is: 136 150 176 44 84.

Question 11

A machine applies one fixed arithmetic operation to every number at each step (study the sample below). What is Step II for the New Input?

Sample Input: 86 42 39 37 38

Step I: 99 55 52 50 51

Step II: 396 220 208 200 204

Step III: 18 4 10 2 6

Step III is the last step of the sample.

New Input: 35 59 41 23 19

  1. 48 72 54 36 32
  2. 192 288 216 144 128
  3. 63 87 69 51 47
  4. 56 80 62 44 40
  5. 12 18 9 9 11
Show the worked solution
  1. Sample Step I: 13 is added to each number (86 → 99).
  2. Sample Step II: each number is multiplied by 4 (99 → 396).
  3. Sample Step III: each number is replaced by the sum of its digits (396 → 18).
  4. Each of those is the only standard operation that turns the previous line into the shown one.
  5. Apply the same steps to the new input: 35 59 41 23 19.
  6. Step I: 48 72 54 36 32
  7. Step II: 192 288 216 144 128
  8. So Step II of the new input is: 192 288 216 144 128.

Question 12

A machine applies one fixed arithmetic operation to every number at each step (study the sample below). What is Step II for the New Input?

Sample Input: 24 75 33 31 29 57

Step I: 72 225 99 93 87 171

Step II: 87 240 114 108 102 186

Step III: 78 42 411 801 201 681

Step IV: 56 8 4 0 0 48

Step IV is the last step of the sample.

New Input: 94 64 93 43 81 58

  1. 282 192 279 129 243 174
  2. 792 702 492 441 852 981
  3. 297 207 294 144 258 189
  4. 141 96 558 258 486 87
  5. 279 189 276 126 240 171
Show the worked solution
  1. Sample Step I: each number is multiplied by 3 (24 → 72).
  2. Sample Step II: 15 is added to each number (72 → 87).
  3. Sample Step III: the digits of each number are reversed (87 → 78).
  4. Sample Step IV: each number is replaced by the product of its digits (78 → 56).
  5. Each of those is the only standard operation that turns the previous line into the shown one.
  6. Apply the same steps to the new input: 94 64 93 43 81 58.
  7. Step I: 282 192 279 129 243 174
  8. Step II: 297 207 294 144 258 189
  9. So Step II of the new input is: 297 207 294 144 258 189.
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Where these questions come from

Most free practice for this topic is a scanned upload or a blog quiz, and neither can tell you a question has exactly one answer. That is the one thing this set can promise: it is minted, not typed. The engine behind it serves DeducePuzzles's daily puzzle round, so the questions here are the same shape as the ones a live round would give you — and there is an unlimited supply of them, which is why this page can be regenerated rather than padded.

If you want the method rather than more questions, All reasoning topics, with the method for each covers the approach, the traps and a worked table. This page and that one deliberately answer different questions: that one is how do I solve these, this one is give me input output reasoning questions with the answers.

FAQ

How do I find the machine's rule?

Compare step one with the input, not the last step with the first. One step shows exactly one operation, and the rule is almost always 'move the largest number to the front' or 'move the alphabetically first word to the end' — or those two alternating. Two steps confirm which.

Do I have to write out every step?

For the last-step and step-count questions, yes — there is no shortcut, and skipping steps is what produces an answer one position off. For a question about a specific step, apply the rule that many times to the input directly rather than working from another step.

Does the machine ever sort in more than one way at once?

In mains-level sets, yes: words from one end and numbers from the other, alternating each step. Determine which element type moves on odd steps and which on even before you continue, because a single misassigned step shifts every later one.

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