# Sunday Times Teaser 3141 – Multiple Extensions

*by Bill Kinally*

#### Published Sunday December 04 2022 (link)

All the phone extensions at Mick’s work place are four-digit numbers with no zeros or twos, and no digit appears more than once in a number. He can enter all the extension numbers on the keypad by starting at key 2 (but not pressing it) then moving in any direction, including diagonally, to an adjacent key and pressing it; then similarly moving to and pressing adjacent keys until the number is entered. A couple of examples of his extension numbers are 3685 and 5148.

He phoned two different extension numbers this morning and later realised that one was an exact multiple of the other.

What was the larger extension number he dialled?

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How long has it been possible for the argument of the ‘difference’ method to be other than a set?

@John From forever!

A rehash of my code borrowing aspects of Brian’s – ‘difference’ method and combinations – but keeping it linear.