# Sunday Times Teaser 3036 – That Old Chestnut

*by Colin Vout*

#### Published Sunday November 29 2020 (link)

Clearing out an old drawer I found a wrinkled conker. It was my magnificent old 6709-er, a title earned by being the only survivor of a competition that I had had with friends. The competition had started with five conkers, veterans of many campaigns; each had begun at a different value between 1300 and 1400.

We used the rule that if an m-er beat an n-er in an encounter (by destroying it, of course!) the m-er would become an m+n+1-er; in effect, at any time the value of a conker was the number of destroyed conkers in all confrontations in its “ancestry”.

I recall that at the beginning of, and throughout, the competition, the value of every surviving conker was a prime number.

What were the values of the five conkers at the start?

Nice work John! I was going to do a version that worked backwards from the last conker but you have beaten me to it!

Thanks Brian,

this should be my final submission on this one. Kindly remove my first two posts (containing the recursive function “conkerwar”).

Brian,

my code above is largely inspired by your solution to Teaser 3029 – Square Jigsaw, a week of Sundays ago.

Thanks!