Brain Teasers

Answers to last issues' teasers separately given


1. Once or twice?

Take 2 identical coins, say Re 1 coins. Hold one firmly on the table
with your finger. Now place the other coin so that it just touches it,
on the left or right. Rotate this coin so that it goes completely around
the first coin, always keeping it in contact. Placing the coins on a
cloth will help prevent them from slipping. While going around, the
coin will also rotate about its centre. For example, if you began with
the coin in the vertical position showing an upright "1", then it will
at one point show an upside-down "1" before it once again rotates to the
upright "1" position. This counts as one rotation of the second coin.

The question is this: when the second coin goes once around the first,
how many full rotations does it make? Some people say once, some people
say twice. How many times do you think? Send in your answer (and your
reasoning) to JM with your name and address!

2. Here is an old game: Ask your friend to think of a number less than
10. Tell your friend to multiply that number by 2, add 2, multiply the
result by 5, add 5, then multiply by 10 and add 10. Finally, you ask him
to tell you just the first digit of the answer. He does not tell you
either the number he had thought of, or the results of any in-between
calculation. Then impress everyone present by telling him which number
he had thought of!!

Can you figure out how this puzzle works?  Do write in and tell us your
answer.