## General puzzles

You are in a game against devil, on a perfectly round table and with an infinite pile of pennies. He says, "OK, we'll take turns putting one penny down, no overlapping allowed, and the pennies must rest flat on the table surface. The first guy who can't put a penny down loses." You can go first. How will you guarantee victory?

Hint
Solution

I guessed 3 natural numbers - x,y,z. You can ask me 2 sums of these numbers with any integer coefficients - (a,b,c). That is, you give me a, b and c and I tell you the result of the expression a*x+b*y+c*z. Seeing the answer, you then give me the 2nd triplet of (a,b,c) & I will tell a*x+b*y+c*z. Give me the algorithm to find x,y and z.

Hint
Solution
Source: Quantnet Forums
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What is/are the next term(s) in the sequence:
a) 1, 11, 21, 1211, 111221, ?
b) 10, 11, 12, 13, 14, 20, 22, 101, ?, ?
c) (This a sequence made by only 2 & 1): 2,2,1,1,2,1,2,2,1, ?, ?....

Hint
Solution
Source: Common
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