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More ways to get Braingle...

Mystery Number

Logic puzzles require you to think. You will have to be logical in your reasoning.

 

Puzzle ID:#35364
Fun:*** (2.22)
Difficulty:*** (3.02)
Category:Logic
Submitted By:cnmne*us*****

 

 

 



There is a 10-digit number, represented by ABCDEFGHIJ, where each numeral, 0 through 9, is used once. Given the following clues, what is the number?

1) A + D = a square number
2) G + J = a triangle number
3) B + I = an even number
4) E * F = an odd number
5) C * H = a prime number
6) A / G = G / C
7) E + I = B + H





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Comments

vlermaAus*
Feb 19, 2007

Too invovled for this time of night and it is sort of out of my abilities. Hate to admit that, but it kind of went right over my head.
scallioAus*
Feb 20, 2007

A most excellent teaser, Cinny! Very, very tough for me... took me a long time and I had to cheat a bit! Math is not my best subject.
peanutAza*
Feb 22, 2007

Brilliant!! Took me close on forever but figured it out

More please..??

peanutAza*
Feb 22, 2007

Brilliant!! Took me close on forever but figured it out

More please..??

ChattyMonkey**
Feb 24, 2007

eeeeekkk!
I'm really bad at these kind!
I did really like it, though.
Good luck with 'em and keep them comin'!
xoxo,
Chatty
Jimbo*au*
Mar 24, 2007

An excellent explanation.
(user deleted)
Apr 09, 2007

whatever!
4demo*
Oct 19, 2007

I finally gave up, but a good teaser for anyone with time and who's unlazy enough to think it through. Difficult but fun!
om123
Jul 12, 2008

wow.. this took FOREVER to do.. i like it tho
(user deleted)
Oct 11, 2008

Dude there is one more answer to the puzzle...and that is 9817453260..
here A=9
B=8
C=1
D=7
E=4
F=5
G=3
H=2
I=6
J=0
A + D = 16, a square no
G + J = 3, a triangle no
B + I = 14, even
E + F = 9, odd
C * H = 2, prime
A/G=G/C=3
E + I = B + H = 10
cnmne*us*
Oct 11, 2008

Clue 4 is E times F equals odd, not E plus F equals odd, so your solution does not work.
javaguru*us*
Jan 08, 2009

Nice teaser and nice explanation, although I think it solves even easier than the explanation. The solution below doesn't require any presumptive assignments.

I started with the same first three observations involving ACDGH.

Then since B and I must either both be even or odd (#3), then H and E must also both be even or odd (#7). Since E and F are odd (#4), then H is also odd.

Now 4 of the 5 odd numbers are accounted for, so B and I are even and AG can't be 9,3 so must be 4,2 which forces the values for D (#1) and J (#2).

This leaves 2 even numbers to assign to B & I and 3 odd numbers to assign to E, F & H. Using the difference between the even numbers forces the choices for E and H (#7), leaving only one choice for F. The remaining prime number is assigned to H (#5) which forces the assignment of the remaining three numbers (#7).

HolografikAbd*
Dec 29, 2011

I think I never heard of triangle numbers before so had to google that.. great teaser though, was quite fun



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