Dear Indrajit and John,
Following John's notation, the product (a1+1)(a2+1)... is odd iff each
ai is even hence the index of the door is a square. Indeed by pairing
only square numbers have an odd number of factors, so there are 31 open
doors and the rest are closed. Its a nice problem to work on
inductively at first as the pattern is fairly accessible, as is the
explanantion (once youve seen it).
Cathy Smith (Homerton College Cambridge)
//
posted from the account of:
-----------------------------------------------------------------------
Nick Goldman, Dept of Zoology, tel: +44-(0)1223-336649
Downing St, Cambridge CB2 3EJ, U.K. fax: +44-(0)1223-336679
[log in to unmask] http://www.zoo.cam.ac.uk/zoostaff/goldman
|