Input–output for SBI PO mains

Input–output looks intimidating: a line of eight or ten jumbled words and numbers, then five or six steps of the "machine" rearranging them. In practice it is one of the most predictable sets in the mains reasoning section. There is one rule, it shows itself in the first two steps, and every question after that is lookup.

The risk is not difficulty but carelessness: misreading which end an element moved to, or losing track of the elements that did not move. This guide shows how to find the rule quickly and how to write steps so you never lose track.

How it is asked

A typical set gives an input and a few steps as an illustration. Then it gives a new input and asks five or so questions about the steps that new input produces:

• How many steps does it take to complete the arrangement?
• Which element is third from the left in Step 4?
• Which step reads "…"?
• How many elements lie between X and Y in the last step?
• Which element is immediately to the right of X in Step 2?

Input–output has appeared more in the mains than in the prelims, but whether a set appears at all changes from year to year.

The common rules

The fourth and fifth rows are the difference that trips people. Always check whether a new element lands at the extreme end or next to the elements already arranged.

A four-check method for finding the rule

1. Input to Step 1: which elements moved, and to which end?
2. Step 1 to Step 2: did the same kind of element move, and did it land at the extreme end or next to the one moved before?
3. What is the order criterion? Largest number, smallest number, alphabetical, reverse alphabetical, word length?
4. Unmoved elements: confirm that they kept their relative order. They almost always do.

Then check the rule against the last illustrated step too. If it fails there, you have picked the wrong criterion.

Worked set 1: placed after the arranged ones

Rule: In each step, the largest remaining number moves to the left, just after the numbers already arranged. The word that comes last in the alphabet moves to the right, just before the words already arranged. Other elements keep their order.

• Input: 34 park 12 lamp 56 zone 27 core
• Step 1: 56 34 park 12 lamp 27 core zone
• Step 2: 56 34 12 lamp 27 core park zone
• Step 3: 56 34 27 12 core lamp park zone

What happened in Step 2? The largest remaining number is 34, and it was already sitting just after 56. So only "park" appears to move. This is a common trap: a step can look as if the rule skipped, when an element was simply already in place.

After Step 3 the numbers read in decreasing order and the words in alphabetical order. The arrangement is complete.

Questions:

1. How many steps are needed? Three.
2. In Step 2, which element is fourth from the left? 56, 34, 12, lamp.
3. In Step 1, which element lies between "lamp" and "core"? 27.

Worked set 2: placed at the extreme ends

Rule: In each step, the smallest remaining number moves to the extreme left, and the word that comes first in the alphabet moves to the extreme right. Other elements keep their order.

• Input: 41 tree 17 bank 63 note 28 lake 52 fish
• Step 1: 17 41 tree 63 note 28 lake 52 fish bank
• Step 2: 28 17 41 tree 63 note lake 52 bank fish
• Step 3: 41 28 17 tree 63 note 52 bank fish lake
• Step 4: 52 41 28 17 tree 63 bank fish lake note
• Step 5: 63 52 41 28 17 bank fish lake note tree

Reading the rule. In Step 1, 17 (the smallest number) went to the extreme left and "bank" (first alphabetically) to the extreme right. In Step 2, 28 went to the extreme left, in front of 17, not after it. Because each new number pushes the earlier ones inwards, the finished numbers read in decreasing order even though the smallest moved first. The words go to the extreme right, so they read in ordinary alphabetical order.

Questions:

1. How many steps are needed? Five.
2. In Step 3, which element is fourth from the right? Counting from the right: lake, fish, bank, 52.
3. In Step 4, how many elements lie between 17 and "bank"? 17 is fourth and "bank" seventh: two (tree and 63).
4. In Step 2, which element is fifth from the left? 28, 17, 41, tree, 63.

Common mistakes

• Choosing the rule from one step. Two steps are the minimum; check a third if you can.
• Mixing up the two placements. "Extreme end" and "next to the arranged ones" give different orders.
• Losing the unmoved elements. Copy them across in their existing order at every step.
• Counting positions from the wrong end. Underline "from the right" in the question.
• Working backwards. A later step does not always tell you the input, because moved elements lose their original positions. If a question asks for the input from a later step, "cannot be determined" is often correct.

Practice set

Use the rule from worked set 2 on this input:

Input: 38 mint 72 gold 15 rose 64 bell 29 kite

1. How many steps are needed to complete the arrangement?
2. Which element is fifth from the right in Step 3?
3. Which step reads "64 38 29 15 72 rose bell gold kite mint"?
4. In Step 2, how many elements lie between 72 and "bell"?
5. In the last step, which element is sixth from the left?
6. In Step 1, which element is immediately to the left of "kite"?
7. In Step 3, which element is third from the left?

The steps:

• Step 1: 15 38 mint 72 gold rose 64 29 kite bell
• Step 2: 29 15 38 mint 72 rose 64 kite bell gold
• Step 3: 38 29 15 mint 72 rose 64 bell gold kite
• Step 4: 64 38 29 15 72 rose bell gold kite mint
• Step 5: 72 64 38 29 15 bell gold kite mint rose

Answers:

1. Five. Five numbers and five words, one of each per step.
2. rose. From the right in Step 3: kite, gold, bell, 64, rose.
3. Step 4.
4. Three: rose, 64 and kite.
5. bell. 72, 64, 38, 29, 15, bell.
6. 29.
7. 15. 38, 29, 15.

What to do next

• Rework both sets from the input line alone, writing every step in columns.
• Do one input–output set a day for two weeks, noting which placement rule each one uses.
• Time yourself: five minutes for a full set, including the questions.
• Input–output sits alongside puzzles in the mains reasoning section. See the reasoning plan for when to practise it.