For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
09/14/2009

PROBLEM # 1
Suppose that P = 2^m and Q = 3ⁿ. What is the value of P²ⁿQ^m?

PROBLEM #2
For k>1, let S_k denote the sum of the k consecutive integers starting with k. Compute the smallest value of k such that S_k is a perfect square.

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Problems from 09/03/09

PROBLEM # 1

What number is 1/3 orf the way from 1/4 to 4/3?

SOLUTION

11/18.

PROBLEM #2

One dimension of the cube is increased by 1, another one is decreased by 1, and the third is left unchanged. The volume of the new rectangular solid is 5less yhan that of the cube. What was the volume of the cube?

SOLUTION
125.

Congratulations to Nikhil Nathwani, Prabhakar Nadkarni and Shailesh Goregaokar, who were the winner of the last set of puzzles.

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