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[thehalibutkid]

Does anyone know how to work out this number? I assume there is some mathematical trickery but don't have the maths fu to work it out. I can offer virtual tea and cuddles to anyone who can answer this for me

Comments

[bethanthepurple]

11 x 11 = 121

[thehalibutkid]

Is that a clue? Or am I being dumb?

[bethanthepurple]

I thought 121 was the answer, but it doesn't work for 7 or 9 :(

Basically, it has to be a multiple of 11, but not of 2-10.

Where is puzzle from?

[thehalibutkid]

It's for a geocache i've been trying to solve for ages.

http://www.geocaching.com/seek/cache_details.aspx?guid=e120bb8b-3ac3-44fe-8eb7-0f615a7a8bfb

I think it's got 5 unique digits and I know it's lower than 50,000

[babysimon]

Do you want (what I think is) the answer?

[thehalibutkid]

Yes please.

[babysimon]

I think the smallest such number is 25201.

Reasoning: The number one less than this has to be divisible by 2, 3, 4... 10. So if we take all the prime factors of the numbers from 2-10, we get 2, 2, 2, 3, 3, 5, 7 (i.e. you can multiply a set of those together to get any number 2-10). Multiply all of those together and we get 2520, the smallest number with all those prime factors and thus the smallest number which can be divided by every number from 2 to 10. Add one and we get a 2521 which leaves remainder one for each of those numbers.

...except that 2521 can't be divided by 11. But the number we're looking for has to be N * 2520 + 1. At which point I cheated and set up a spreadsheet to calculate (N * 2520 + 1)/11, and the smallest N giving a whole result is 10, giving us a final number 25201. Probably there's some clever way to work out the last bit directly...

[babysimon]

If it needs to have 5 unique digit, my spreadsheet also gives 80641 (after 52921 as well). But maybe that's too big?

[fruit_boy]

Hey you.....

HAPPY BIRTHDAY