Input-Output (Machine)

Subject: Reasoning | Frequency: 1-2 questions per APPSC paper | Time: 60-90 sec/question

Introduction

A "machine" takes an input (a line of words and/or numbers) and rearranges it step by step following a specific rule until it reaches a final output. You must identify the rule and predict intermediate or final steps. APPSC commonly tests alternating word-number sorting. The key: spend 60 seconds understanding the rule by comparing Input to Step 1 to Step 2 — once the rule is clear, applying it is mechanical.

Core Method

1. Compare Input to Step 1 — what changed? Which element moved? Where did it go?
2. Compare Step 1 to Step 2 — does the same pattern continue?
3. Identify the rule:
   • Alphabetical ordering of words?
   • Numerical ordering (ascending/descending)?
   • Alternating (word then number)?
   • Mathematical operation on numbers?
4. Verify the rule across all given steps
5. Apply the rule to predict the requested step

Time-Saving Tip

Write only the first letter of each word instead of the full word when tracking steps.

Types

Type 1: Ordering/Sorting

Words arranged alphabetically, numbers ascending/descending. One element placed per step.

Type 2: Shifting

Elements shift positions (e.g., last moves to first, first-last swap).

Type 3: Mathematical Operations

Numbers modified each step (digit sum, rounding, multiplication).

Type 4: Alternating Arrangement

Words and numbers placed alternately — smallest number and first alphabetical word alternately.

Type 5: Custom Rules

Unique patterns specific to the problem.

Worked Examples — Easy

Q1: Identify the rule:

• Input: now 32 come 18 after 45 deep 11
• Step 1: after now 32 come 18 45 deep 11
• Step 2: after 11 now 32 come 18 45 deep
• Step 3: after 11 come now 32 18 45 deep

Rule: Alternately picks (1) alphabetically first remaining word (odd steps) and (2) smallest remaining number (even steps), placing each at the leftmost available position.

Q2: What would be Step 4 of: Input: great 49 land 17 open 28 each 35

• Step 1: each great 49 land 17 open 28 35 (first word: "each")
• Step 2: each 17 great 49 land open 28 35 (smallest number: 17)
• Step 3: each 17 great 49 land open 28 35 → next word: "great" already placed. Next unplaced word: "land"
• Step 3: each 17 great land 49 open 28 35
• Step 4: each 17 great 28 land 49 open 35 (next number: 28)
• Answer: each 17 great 28 land 49 open 35

Q3: Shifting rule: Input: A B C D E F

• Step 1: F A B C D E (last to first)
• Step 2: E F A B C D (last to first again)
• Step 3: D E F A B C

Worked Examples — Medium

Q4: Sorting rule:

• Input: 7 3 9 1 5 8
• Step 1: 1 7 3 9 5 8 (smallest to front)
• Step 2: 1 3 7 9 5 8 (next smallest to 2nd)
• Step 3: 1 3 5 7 9 8 (next smallest to 3rd)
• Step 4: 1 3 5 7 8 9 (complete sort)

Q5: Mathematical rule:

• Input: 26 34 56 78 63 99
• Step 1: 20 30 50 70 60 90
• Rule: Subtract unit digit from each number (round down to nearest 10)
• 26-6=20, 34-4=30, 56-6=50, 78-8=70, 63-3=60, 99-9=90

Q6: Digit sum rule:

• Input: cat 15 dog 28 eat 36 fun 42
• Step 1: cat 6 dog 28 eat 36 fun 42 (15: 1+5=6)
• Step 2: cat 6 dog 10 eat 36 fun 42 (28: 2+8=10)
• Step 3: cat 6 dog 10 eat 9 fun 42 (36: 3+6=9)
• Step 4: cat 6 dog 10 eat 9 fun 6 (42: 4+2=6)

Worked Examples — Hard

Q7: Complex alternating rule:

• Input: 15 join 24 help 38 more 46 know
• Step 1: help 15 join 24 38 more 46 know (first alphabetical word to front)
• Step 2: help 46 15 join 24 38 more know (largest number to 2nd)
• Step 3: help 46 join 15 24 38 more know (next alphabetical word to 3rd)
• Step 4: help 46 join 38 15 24 more know (next largest to 4th)
• Step 5: help 46 join 38 know 15 24 more (next word to 5th)
• Step 6: help 46 join 38 know 24 15 more (next number to 6th)
• Step 7: help 46 join 38 know 24 more 15 (final)
• Rule: Alternately place first alphabetical word and largest remaining number

Q8: Using the rule from Q7, input "54 park 17 rain 83 soft 29 time". Step 5?

• Step 1: park 54 17 rain 83 soft 29 time
• Step 2: park 83 54 17 rain soft 29 time
• Step 3: park 83 rain 54 17 soft 29 time
• Step 4: park 83 rain 54 17 soft 29 time (54 already positioned)
• Step 5: park 83 rain 54 soft 17 29 time
• Answer: park 83 rain 54 soft 17 29 time

Shortcuts & Tricks

Common Mistakes

1. Missing the alternating pattern — many machines alternate between word and number operations
2. Losing track of positions — shifted elements change ALL subsequent positions
3. Wrong sorting direction — ascending vs descending; alphabetical vs reverse
4. Not verifying across steps — rule must hold for ALL given steps
5. Confusing "next step" with "final output" — Step 3 is not necessarily the final output

Exam Strategy

• Spend 60 seconds understanding the rule by comparing Input → Step 1 → Step 2
• Once the rule is clear, applying it is mechanical
• APPSC keeps difficulty at medium
• Time: 60-90 seconds per question
• The most common rule is alternating word-number sorting
• Negative marking: -0.333 — verify the rule across at least 2 steps before applying

Practice Questions

1. Input: 5 2 8 1 9. Rule: smallest to front each step. Step 2? → Step 1: 1 5 2 8 9, Step 2: 1 2 5 8 9
2. Input: A B C D. Rule: first and last swap. Step 1? → D B C A
3. Input: red 5 blue 3 green 7. Rule: alphabetical word first, ascending number second, alternating. Step 2? → Step 1: blue red 5 3 green 7, Step 2: blue 3 red 5 green 7
4. How many steps to sort 6 elements? → Maximum 5 steps
5. Input: 48 27 63 15. Rule: subtract digit sum. Step 1? → 48-12=36, 27-9=18, 63-9=54, 15-6=9 → 36 18 54 9

Key Terms / Formulas