For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
12/07/2010

PROBLEM # 1
What is the area of the largest square that can be completely inscribed in a triangle whose sides 3,4 and 5 inches?

PROBLEM #2
A rectangular sheet of paper is folded so that two diagonally opposite corners come together. If the crease formed is the same length as the longer side of the sheet, what is the ratio of the longer side of the sheet to the shorter side?

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Problems from 11/25/10

PROBLEM # 1

How many outlines of triangles of all sizes and shapes can you trace in Figure 1?

SOLUTION
37.

PROBLEM #2

In a 52 card deck, how many 5-card hands have a single pair and no 3-of-a-kind or 4-of-a-kind?

SOLUTION

Congratulations to Arul Prakashi, who was the winner of the last set of puzzles.

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