For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
06/03/2014

PROBLEM #1

"Sister, you have as many brothers as you have sisters." "Brother, you have twice as many sisters as you have brothers." Can you deduce from this conversation how many children there are in the family?

PROBLEM #2

A shopkeeper wants to be able to dispense sugar in whole pounds ranging from one pound up to 40 pounds. He has a standard, equal-arm balance weigh scale. Being of an extremely economical outlook, he wants to use the least possible number of weights to enable him to weigh any number of pounds between 1 and 40. How many weights does he need and what are they?

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Problems from 05/22/14

PROBLEM #1
Find all pairs of positive integers, x, y, such that x2 + 3y and y2 + 3x are both perfect squares.

Solution

PROBLEM #2

A solid sphere of radius 15cm is recast into solid circular cones of radius 2.5cm and height 8cm. How many cones do we get?

Solution

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