### Easy as π

#### by subacati

Do you have enough brain cells? :p. …

There is a 10-digit mystery number (no leading 0), represented by ABCDEFGHIJ, where each numeral, 0 through 9, is used once. Given the following clues, what is the number?

A + B + C + D + E is a multiple of 6.

F + G + H + I + J is a multiple of 5.

A + C + E + G + I is a multiple of 9.

B + D + F + H + J is a multiple of 2.

AB is a multiple of 3.

CD is a multiple of 4.

EF is a multiple of 7.

GH is a multiple of 8.

IJ is a multiple of 10.

FE, HC, and JA are all prime numbers.

The Answer is 5736912480

A = 5, B = 7, C = 3, D = 6, E = 9, F = 1, G = 2, H = 4, I = 8, J = 0

5 + 7 + 3 + 6 + 9 = 30, which is a multiple of 6.

1 + 2 + 4 + 8 + 0 = 15, which is a multiple of 5.

5 + 3 + 9 + 2 + 8 = 27, which is a multiple of 9.

7 + 6 + 1 + 4 + 0 = 18, which is a multiple of 2.

57 is a multiple of 3.

36 is a multiple of 4.

91 is a multiple of 7.

24 is a multiple of 8.

80 is a multiple of 10.

19, 43, and 05 are prime numbers.

A) The sum of digits 0 through 9 is 45. To satisfy Conditions 1 and 2, a pair of multiples must equal 45. The only pair that satisfies those conditions are 30 (multiple of 6) and 15 (multiple of 5). Likewise, to satisfy Conditions 3 and 4, the pair of multiples must be 27 (multiple of 9) and 18 (multiple of 2).

B) Make lists of the multiples of 3, 4, 7, 8, and 10 (for Conditions 5 through 9). Delete multiples whose digits are the same (33, 44, 66, 77, 88, 99).

C) To satisfy Condition 9, J must be 0. Delete multiples that require 0 in a different location. For JA to be prime (Condition 10), A must be: 2, 3, 5, or 7. Delete multiples of 3 that have another digit for A.

D) For FE and HC to be prime (Condition 10), C and E can not be even or 5. Delete multiples of 4 and 7 that have another digit for C and E.

E) Per Condition 4, B + D + F + H + J = 18. D, H, and J must be even (required to form multiples of even numbers). To attain the sum of 18 (an even number), B and F must either be both odd or both even. If both are even, then the sum of those five digits would be 20. B and F must be odd. Delete multiples of 3 and 7 that have an even digit for B and F. The only remaining multiple of 7 is 91. E is 9 and F is 1. Delete multiples that require 1 or 9 in a different location.

F) The only remaining options for AB contain 7. Delete multiples that require 7 in a different location. The only remaining options for CD contain 3. Delete multiples that require 3 in a different location.

G) To satisfy Condition 1, CD must be 36 and AB must be either 57 or 75. C is 3 and D is 6. Delete multiples that require 5, 6, or 7 in a different location.

H) The only remaining options for GH contain 4. Delete multiples that require 4 in a different location.

I) Per Condition 3, A + C + E + G + I = 27. Since C =3 and I = 9, the other three must total 15. There is only one combination of remaining multiples (57, 24, and 80) that can satisfy this condition. A is 5, G is 2, and I is 8. B is 7 and H is 4.

:)*A :angel: cheated but has it…. :p *I asked for help…. not enough brain cells ! 😆

Quick question. Does AB mean A multiplied by B like it would in most algebraic notation? Because if it does this can't actually be worked out. However, if it's just one number in front of the other (A=1 B=2 so AB=12) then I think I've got it.

Hey, whisper notations are working again. Typically I've forgotten what I was going to change mine to now. :irked:

Nope, I don't have enough brain cells. :p 😀

My brain cells are still on summer vacation 😆 😆

Originally posted by Furie:

Correct! :up:.I'll put the full sollution up later to give others a chance to try! :p.

Originally posted by qlue:

admit you will cheat as I did! 😆

Originally posted by ellinidata:

Who says I even tried? :angel:.

😆 I always admired you honesty! :up:

:irked: That's twice now that you don't say anything to my comments I leave. Sorry to bother you. I'll go now and not come back.

Originally posted by Furie:

Looks that way! :left:.

Am I the only one bothering? 😡

Originally posted by Dacotah:

My appologies. I don't mean to offend anyone. :awww:.I usually only make a specific reference to a comment if I have a pertinent response to add. :left:.I'm not ignoring you, I simply had nothing to add.

Originally posted by Furie:

correction,you are the only one with brain cells left! *respect*:p

It only takes 15 minutes folks. Hell, the clues immediately tell you where the zero goes so you've only got nine left to figure out.

I've posted the full answer, only Mik got the answer. (It was kind of a 'one horse race' though :rolleyes:)

On a second thought… :whistle:

With a mane like that? :whistle:.

:sst: he don`t look like a horse to me but if you insist…. :left::whistle:

We all use math everyday. To predict weather, to tell time, to handle money. Math is more than just formulas and equations. It's using your mind to unlock the biggest mysteries we know.

Originally posted by Furie:

+1Mostly I agree. Although it's formulae and equations that give maths it's analytical properties. :up:.Originally posted by Furie:

Maths has yet help me understand Women. :awww:. (or people in general for that matter.)P.S: I've discovered that the formula I was trying to apply in that other post was the wrong formula. Now I just need to find the correct formula for the type of neural network I'm using. :rolleyes:.

Search for my last comment on Google. 😉

I'll see if I can find a boxed set! :up:.

My first attempt to do that yeilds this result,

Is this what I was meant to find? :left:.Or were to trying to show me this? :left:.

The first. Good show if a little formulaic at times.