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Editorial Team
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Asked: 2026-05-17T02:29:55+00:00

I can have any number row which consists from 2 to 10 numbers. And

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I can have any number row which consists from 2 to 10 numbers. And from this row, I have to get geometrical progression.

For example:
Given number row: 125 5 625 I have to get answer 5. Row: 128 8 512 I have to get answer 4.

Can you give me a hand? I don’t ask for a program, just a hint, I want to understand it by myself and write a code by myself, but damn, I have been thinking the whole day and couldn’t figure this out.

Thank you.

DON’T WRITE THE WHOLE PROGRAM!

Guys, you don’t get it, I can’t just simple make a division. I actually have to get geometrical progression + show all numbers. In 128 8 512 row all numbers would be: 8 32 128 512

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1 Answer

  1. Editorial Team

    Seth’s answer is the right one. I’m leaving this answer here to help elaborate on why the answer to 128 8 512 is 4 because people seem to be having trouble with that.

    A geometric progression’s elements can be written in the form c*b^n where b is the number you’re looking for (b is also necessarily greater than 1), c is a constant and n is some arbritrary number.

    So the best bet is to start with the smallest number, factorize it and look at all possible solutions to writing it in the c*b^n form, then using that b on the remaining numbers. Return the largest result that works.

    So for your examples:

    125 5 625

    Start with 5. 5 is prime, so it can be written in only one way: 5 = 1*5^1. So your b is 5. You can stop now, assuming you know the row is in fact geometric. If you need to determine whether it’s geometric then test that b on the remaining numbers.

    128 8 512

    8 can be written in more than one way: 8 = 1*8^1, 8 = 2*2^2, 8 = 2*4^1, 8 = 4*2^1. So you have three possible values for b, with a few different options for c. Try the biggest first. 8 doesn’t work. Try 4. It works! 128 = 2*4^3 and 512 = 2*4^4. So b is 4 and c is 2.

    3 15 375

    This one is a bit mean because the first number is prime but isn’t b, it’s c. So you’ll need to make sure that if your first b-candidate doesn’t work on the remaining numbers you have to look at the next smallest number and decompose it. So here you’d decompose 15: 15 = 15*?^0 (degenerate case), 15 = 3*5^1, 15 = 5*3^1, 15 = 1*15^1. The answer is 5, and 3 = 3*5^0, so it works out.

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