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For The Mathematically Inclined

Anil Saigal

There is a number that is 5 times the sum of its digits. What is this number?

I have a miniature Pyramid of Egypt. It is 4 inches in height. I was invited to display it at an exhibition. I felt it was too small and decided to build a scaled-up model of the Pyramid out of material whose density is (1 / 4) times the density of the material used for the miniature. I did a "back-of-the-envelope" calculation to check whether the model would be big enough.

If the mass (or weight) of the miniature and the scaled-up model are to be the same, how many inches in height will be the scaled-up Pyramid? Give your answer to two places of decimal.


Please send your solutions to anil@lokvani.com.

Use Problem Solutions M-031810 as the subject line. Please include your full name in the text of the main message. Everyone with the right answer will be acknowledged in the next issue of Lokvani.

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Problems from 03/04/10


The founders of Hairytown decreed years ago that:

1. No two people can have the same number of hairs
2. No one can have 999 hairs.
3. No one can have more than, or the same number of hairs as, the population of the town




You intend to fly non-stop around the world.  But you can only go halfway around the world on a full tank. However you can arrange many planes exactly like yours to assist with refuelling. Assuming refuelling can be done midair, ignoring refuelling and turning time, and without crashing any plane, what is the minimum number of planes you will need?


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