Each of the triangular numbers that are below 1000 is written on a separate card. Some of these cards are then placed in a circle so that, viewed from the center, the righthand digit of each card matches the lefthand digit of the card to its right. No tricks are used such as turning a card upsidedown.
What's the maximum number of digits that can appear on such a subset of the cards?
There are 44 triangular numbers below 1000.
Of these 16 either begin and/or end with 1, 3, 5, 6 or 8:
15, 36, 55, 66, 105, 136, 153, 171,
325, 351, 378, 528, 561, 595, 666, 861.
In the instance of 8 only one number begins with it, thus there can be only one pairing for it, hence only either 378 or 528 may be used but not both.
I propose, initially at least:
153, 325, 55, 595, 528, 861, 171, 105 and 561.
This uses 9 of my selected 16 and has 26 digits.
Edited on January 10, 2008, 7:57 am

Posted by brianjn
on 20080109 21:23:30 