Input-output questions present a sequence of words, numbers, or symbols that a machine rearranges through several steps. The machine follows a consistent hidden rule. Your job is to discover that rule from the shown steps and apply it accurately.

1. Common machine patterns

• Sorting: the smallest or largest remaining item moves into its final position at each step.
• Alternating placement: the machine places the smallest, then largest, then next smallest item.
• Word ordering: words may be arranged alphabetically, by length, or by first or last letter.
• Number operations: digits may be reversed, added, multiplied, or replaced by related values.
• Mixed sequences: numbers and words can follow separate rules within the same row.

2. How to identify the rule

1. Compare the input with Step I and identify exactly what moved or changed.
2. Compare Step I with Step II to see whether the same action repeats.
3. Mark items that have reached their final positions; many machines leave them fixed.
4. Test the rule on every given step before applying it to a new input.
5. Write the sequence position by position rather than relying on memory.

3. Sorting rules

In a common arrangement machine, one item is placed correctly at each step. For ascending order, the smallest remaining value moves left; for descending order, the largest remaining value moves left. The untouched items retain their relative order unless the displayed steps show otherwise.

4. Word and symbol rules

• For alphabetical order, compare letters from left to right; a shorter word comes first when one is a prefix of another.
• For word length, check whether ties keep their original order or are resolved alphabetically.
• For letter transformations, convert letters to positions when shifts are difficult to spot.
• For symbols, check count, repetition, position, and direction before assuming an arithmetic rule.

Common mistakes

• Guessing the final order without first proving the step-by-step rule.
• Changing the order of items that the machine has not moved.
• Confusing ascending with descending order after observing only one step.
• Ignoring tie-breaking rules for words of the same length or numbers with the same property.
• Answering from the wrong step when the question asks for an intermediate output.

Quick revision summary

• Infer one repeated operation from consecutive steps.
• Track fixed positions and the remaining unsorted items separately.
• Verify a rule against every shown transition.
• Apply the rule one step at a time to avoid rearrangement errors.