For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
03/27/2014

PROBLEM #1

The minute hand of a clock is twice as long as the hour hand. At what time, between 00:00 and when the hands are next aligned (just after 01:05), is the distance between the tips of the hands increasing at its greatest rate?

PROBLEM #2

Triangle ABC is isosceles with AB = AC. Point D on AB is such that

BCD = 15Â° and BC =

AD. What is

CAB?

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Problems from 03/13/14

PROBLEM #1
What is the area of the largest semicircle that can be inscribed in the unit square?

Solution
0.539012

PROBLEM #2

A perfect square has length n if its last n (decimal) digits are the same and non-zero. What is the maximum possible length?

Solution
Â±38 (mod 500.)

Congratulations to Abhimanyu Bhargava, who was the winner of the last set of puzzles. Here are two puzzles for one and all!

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