DeduceEXAM-GRADE DAILY REASONING

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 Deduce 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 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: 69 65 mango forest 11 wagon

Step I: mango 69 65 forest 11 wagon

Step II: mango wagon 69 65 forest 11

Step III: mango wagon forest 69 65 11

Step III is the last step of the sample.

New Input: 31 garden stone 84 98 grape

  1. 3
  2. 1
  3. 2
  4. 4
  5. 5
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: 31 garden stone 84 98 grape.
  4. Step I: grape 31 garden stone 84 98
  5. Step II: grape stone 31 garden 84 98
  6. Step III: grape stone garden 31 84 98
  7. The arrangement is complete after Step III, so the machine needs 3 steps.

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: ocean 77 32 jungle 66 garden

Step I: ocean garden 77 32 jungle 66

Step II: ocean garden jungle 77 32 66

Step II is the last step of the sample.

New Input: 41 flute 80 orbit 12 rock

  1. 41 80 12 flute orbit rock
  2. rock orbit 41 flute 80 12
  3. flute orbit 12 rock 41 80
  4. 80 41 12 flute orbit rock
  5. rock flute 41 80 orbit 12
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: 41 flute 80 orbit 12 rock.
  4. Step I: rock 41 flute 80 orbit 12
  5. Step II: rock flute 41 80 orbit 12
  6. So Step II of the new input is: rock flute 41 80 orbit 12.

Question 5

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: 43 30 14 lamp candle quilt

Step I: lamp 43 30 14 candle quilt

Step II: lamp quilt 43 30 14 candle

Step III: lamp quilt candle 43 30 14

Step III is the last step of the sample.

New Input: 27 46 jungle yard zebra 71

  1. 5
  2. 3
  3. 1
  4. 4
  5. 2
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: 27 46 jungle yard zebra 71.
  4. Step I: yard 27 46 jungle zebra 71
  5. Step II: yard zebra 27 46 jungle 71
  6. Step III: yard zebra jungle 27 46 71
  7. The arrangement is complete after Step III, so the machine needs 3 steps.

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: quilt 81 92 forest 57 pearl river

Step I: pearl quilt 81 92 forest 57 river

Step II: pearl quilt river 81 92 forest 57

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

New Input: 32 mango hill 73 lotus lamp 51

  1. 6
  2. 3
  3. 5
  4. 4
  5. 2
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: 32 mango hill 73 lotus lamp 51.
  4. Step I: hill 32 mango 73 lotus lamp 51
  5. Step II: hill lamp 32 mango 73 lotus 51
  6. Step III: hill lamp lotus 32 mango 73 51
  7. Step IV: hill lamp lotus mango 32 73 51
  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: bridge 23 grape 83 60

Step I: 23 bridge grape 83 60

Step II: 23 60 bridge grape 83

Step III: 23 60 83 bridge grape

Step III is the last step of the sample.

New Input: valley 20 61 island 50

  1. 20 50 valley 61 island
  2. 20 61 50 valley island
  3. 20 island valley 61 50
  4. valley island 20 50 61
  5. island 20 valley 61 50
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: valley 20 61 island 50.
  4. Step I: 20 valley 61 island 50
  5. Step II: 20 50 valley 61 island
  6. So Step II of the new input is: 20 50 valley 61 island.

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: 35 97 bridge 74 drum

Step I: 35 bridge 74 drum 97

Step II: 35 bridge drum 74 97

Step III: bridge drum 35 74 97

Step III is the last step of the sample.

New Input: 49 73 needle 72 lotus

  1. lotus needle 49 72 73
  2. needle lotus 49 73 72
  3. 49 needle lotus 72 73
  4. 49 lotus 72 73 needle
  5. lotus needle 49 73 72
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: 49 73 needle 72 lotus.
  4. Step I: 49 needle 72 lotus 73
  5. Step II: 49 needle lotus 72 73
  6. So Step II of the new input is: 49 needle lotus 72 73.

Question 9

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: 72 jungle 36 kettle wagon 52

Step I: wagon 72 jungle 36 kettle 52

Step II: wagon jungle 72 36 kettle 52

Step III: wagon jungle kettle 72 36 52

Step III is the last step of the sample.

New Input: 65 81 62 queen house garden

  1. 1
  2. 5
  3. 4
  4. 3
  5. 2
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: 65 81 62 queen house garden.
  4. Step I: house 65 81 62 queen garden
  5. Step II: house queen 65 81 62 garden
  6. Step III: house queen garden 65 81 62
  7. The arrangement is complete after Step III, so the machine needs 3 steps.

Question 10

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 84 bridge orbit 42 25

Step I: orbit pearl 84 bridge 42 25

Step II: orbit pearl bridge 84 42 25

Step II is the last step of the sample.

New Input: 40 jam valley piano 85 73

  1. jam 40 piano valley 85 73
  2. jam piano 40 valley 85 73
  3. 40 valley 85 73 piano jam
  4. 40 jam 73 piano valley 85
  5. 40 73 85 jam valley piano
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: 40 jam valley piano 85 73.
  4. Step I: jam 40 valley piano 85 73
  5. Step II: jam piano 40 valley 85 73
  6. So Step II of the new input is: jam piano 40 valley 85 73.

Question 11

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: forest 33 90 15 piano garden

Step I: piano forest 33 90 15 garden

Step II: piano forest garden 33 90 15

Step II is the last step of the sample.

New Input: 20 59 kettle jam kite 83

  1. 4
  2. 2
  3. 3
  4. 1
  5. 5
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: 20 59 kettle jam kite 83.
  4. Step I: jam 20 59 kettle kite 83
  5. Step II: jam kite 20 59 kettle 83
  6. Step III: jam kite kettle 20 59 83
  7. The arrangement is complete after Step III, so the machine needs 3 steps.

Question 12

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 river jungle yard dew 53 46

Step I: dew 70 river jungle yard 53 46

Step II: dew yard 70 river jungle 53 46

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

New Input: 72 hill 58 16 nest valley stone

  1. valley stone 72 hill 58 16 nest
  2. hill 16 72 58 nest valley stone
  3. hill nest 16 valley stone 58 72
  4. hill nest 72 58 16 valley stone
  5. 16 hill 72 58 nest valley stone
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: 72 hill 58 16 nest valley stone.
  4. Step I: hill 72 58 16 nest valley stone
  5. Step II: hill nest 72 58 16 valley stone
  6. So Step II of the new input is: hill nest 72 58 16 valley stone.
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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 Deduce'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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