BTW: All of the people mentioned in the problems are mountain climbers.
All but Georgie Mallory have climed Everest. (Malory almost certainly did not, he died trying.)
George Mallory wants you to show by induction that + n is evenly divisibleby 2, for all n ≥ 1
We first check that + n is evenly divisibleby 2 for n = 1. But 1 + 1 = 2, which is diviible by 2.
Now assume that + n is divisible by 2. And Look at
+ (n+1) = + 2 n + 1 + n + 1 = + n + 2n + 2
By induction + n is divible by 2. 2n + 2 is divisible by 2, therefore
the sum is divisible by 2, and the result follows.
Edmond Hillary want you to show (you need not use induction) that n! ≤ for all n ≥ 1.
Lopsang Jangbu Sherpa needs to know: In a committe of size n ≥2, how many way are there to
create two subcommitees A and B, each with a designated member called the
chair,such that each person can be on 0,1,or 2 subcommittees,but the chair of subcommitte A cannot be the member of subcommitee B and the chair of committee B cannot be a memeber of committee A?
Pick the chair of committee A, there are n ways to do this. Pich the chiari of committe B, there are n-1 ways to do this. There are (n-2) people left weach ofwhich can serve
on none, A, B, or AB. Therefore there are 4 choices.
Answer is ........ n(n-1)
Anatoli Boukreev wants to know how many ways are there to get 7 cards (out of 52) with 3 cards of one rank, 2 cards of another rank,
the rest of the cards unrelated (xxxyyzwr).