Math Puzzle: Solution

By Sebastiaan

This is the solution to this post.

The answer is 22 hours.

You can look at it in different ways, for example: n₀ = 1. Then n_i+1 = n_i * 3 + 1. So then we just enter the numbers, and work our way towards the answer.

One could also get the following formula: n_i+1 = 4*n_i - 3*n - 3 with n₀ = 1.

Lets take a closer look a the second formula. If you take a big n, say, 20, what does it look like? If n is that big, the second term (3*n) is insignificant, not even speaking of - 3. But what is 4*n_i? It's four times the previous n, which is four times the previous n, etc... The first term is 4*1 (so, 4¹), the second 4*4 (so, 4²), the third is 4*16, you can guess where we're going: 4ⁿ. This is a quick way to see how fast this progresses, within a day everyone knows what the secret is. But it does not provide you with the exact answer (22), since it's only an estimate.

If you calculate exactly, or use something like this calculating programme, you can easily find the answer. First number would be 1, the common ratio 3, and n is 22. Try progressing n up to 22, and see how fast it goes up.