General puzzles




Medium General

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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Medium General

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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