For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
03/04/2014

PROBLEM #1

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

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?

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Problems from 02/27/14

PROBLEM #1
I have ten boxes which I want to pack into crates. Each crate can carry a maximum of 25 kg. But I only have three crates, and the total weight of the boxes is 75kg:

15 kg, 13kg, 11 kg, 10 kg, 9 kg, 8 kg, 4 kg, 2 kg, 2kg, 1 kg

How can I pack the boxes into the crates?

Solution
Crate 1:(15kg, 10kg), Crate 2:(13kg, 8kg, 4kg), Crate 3:(11kg, 9kg, 2kg, 2kg, 1kg).

PROBLEM #2

A person drove 120 miles at 40mph, then drove back the same 120 miles at 60mph.What was the average speed for the trip.

Solution
48 mph.

Congratulations to Kishore Balsara, Abhimanyu Bhargava, Moushami Katragadda and Aashutosh Soni, who were the winners of the last set of puzzles. Here are two puzzles for one and all!

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