the underground temple of the lost civilisation of the ancient primes was recently discovered deep in a south american jungle. the jeys to the temple were discovered long ago. There are 25 of them, each one numbered with a different prime eless than 100.
Each of the temple's doors has a lock which requires a set of keys to open it. The numbers on the keys which open a lock always add to 100, the sacred number of the ancient primes.
the keys which open the outer door of the temple are numbered 2,3,5,7,11,13,17,19,23. Doors to unimportant rooms inside need only two keys to open them: the broom cubbaord needs 3 and 97 and the laundry 17 and 83
a) show that no door can be unlocked with exactly eight keys.
(there are exactly 35 selections of seven keys which add to 100. so it is not surprising that the temple's main chanber ahs 35 entry doors each needing a different selection of seven keys to open it)
b) all of these 35 doors are eventually opened. find the selection of keys used on one of these doors which contains the key with the highest number
c) find the selection of seven keys whose numbers have the largest product
any help is much much appreciated....this problem is super hard >.<