What is asked
A machine rearranges an input line of words and/or numbers one step at a time. You see an illustration (input plus all steps) and then a new input; questions ask what a particular step looks like, how many steps are needed, or which element is k-th from an end in some step. Mains often uses number machines with arithmetic operations stated in words.
Common rules
- Dictionary order: in each step the next word alphabetically is placed at the left end (just right of the words already arranged); the rest shift right keeping their order.
- Words and numbers together: in each step one word goes to the left side (alphabetical) and one number to the right side (descending, so the right end ends up ascending).
- Number operations: reverse digits, sort, add/subtract based on odd or even, replace by digit sum.
- Variations: by number of letters in a word, by first letter, largest number placed first, etc.
Method
- Compare the input with Step I of the illustration: which element moved, and to which end? Confirm with Step II.
- Check how the untouched elements behave: usually they keep their relative order and just shift.
- Count the steps of the illustration to see when the machine stops (when the arrangement is complete).
- Apply the rule to the new input, writing every step - do not skip steps mentally.
Worked example
Rule: each step puts the next word in dictionary order at the left end. Input: night apple sugar mango fresh colour bread house.
| Step I | apple night sugar mango fresh colour bread house |
|---|---|
| Step II | apple bread night sugar mango fresh colour house |
| Step III | apple bread colour night sugar mango fresh house |
Continuing, fresh (Step IV), house (Step V) and mango (Step VI) are placed; night and sugar are already in order, so Step VI is the last step.
Time target
Writing all steps takes 2-3 minutes; after that each question takes 15-20 seconds. A complete step table is worth the time because all five questions use it.