For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
05/20/2014

PROBLEM #1

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

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?
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Problems from 05/08/14

PROBLEM #1

A quart bottle contains a mixture that is 1/3 antifreeze, 2/3 water. A half gallon bottle contains a mixture that is 3/4 antifreeze, 1/4 water. The contents of the two bottles are poured into a gallon jug. What is the ratio of antifreeze to water in the jug?

Solution
11:7.

PROBLEM #2

A group of children share marbles from a bag. The first child takes one marble and a tenth of the remainder. The second child takes two marbles and a tenth of the remainder. The third child takes three marbles and a tenth of the remainder. And so on until the last child takes whatever is left. Knowing that all the children end up with the same number of marble, how many children were there and how many marbles did each one get?

Solution

9 children and 81 marbles.

Congratulations to Kishore Balsara and Anindya Basu, who were the winners of the last set of puzzles. Here are two puzzles for one and all!

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