# Counterfeit Coin problem with a twist?

We all know the counterfeit coin problem with 7 real coins & one fake one.

n coins = x weighings

2 coins = 1 weighing

3 coins = 1 weighing

4 coins = 2 weighings

5 coins = 2 weighings

6 coins = 2 weighings

7 coins = 2 weighings

8 coins = 2 weighings

9 coins = 2 weighings

10 coins = 3 weighings

11 coins = 3 weighings

12 coins = 3 weighings

etc.

Well I get the problem and I sort of have the answer to it.

n^2 = k & the amount of digits k has = x weighs

How do I explain that in one equation/math sentence?

like n^2 x 3^3 or something like that…

Help please. Thanxx =]

I know how to solve it.

I just need to know how to put that the number of digits n^2 has is the amount of weighings or x

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n/2^k =< 2

think about how you actually perform the weighings.

You divide the coins in half, and in half again. that first weighing tells you which half has the odd coin. You repeat until you have two coins left.