[RESOLVED] a Maths problem - urgent please

[Harsh Gupta]

consider A to I. The values of A to I are equal to 1 to 9, not necessarily in sequential manner. And A=4. Now
A+B+C+D = D+E+F+G = G+H+I = 17.
What is the value of D,G.

could somebody please tell me how to do this?? i am totally lost on this one.

[Logophobic]

Edit: Please ignore this post. The real solution is in the following post.

Take each group individually:
Group 1: B+C+D=13
(1a) 9+3+1
(1b) 8+3+2
(1c) 7+5+1
(1d) 6+5+2

Group 2: D+E+F+G=17
(2a) 9+5+2+1
(2b) 8+6+2+1
(2c) 8+5+3+1
(2d) 7+6+3+1
(2e) 7+5+3+2

Group 3: G+H+I=17
(3a) 9+7+1
(3b) 9+6+2
(3c) 9+5+3
(3d) 8+7+2
(3e) 8+6+3

Find a solution from group 2 with exactly one overlap on a solution from each of groups 1 and 3 where there is no overlap between the solutions taken from groups 1 and 3.

[Andy_P]

Since A to I are 1 to 9, then: A+B+C+D+E+F+G+H+I = 45

We know that: A+B+C+D + D+E+F+G + G+H+I = 51 (17+17+17)

Therefore the difference between the two is D+G, so D+G = 51-45 = 6

Only two pairs of numbers can add together to form 6: 1 and 5, or 2 and 4.

The correct pair must be 1 and 5 because we know A = 4.

If we guess that D=1 and G=5, then 4+B+C+1 = 17 and 5+H+I = 17

This means that B+C = 17-4-1 = 12, and H+I = 17-5 = 12.

Three pairs of numbers add together to make 12: 3+9, 4+8, and 5+7.

Of these, it can't be 4+8 because A=4, and it can't be 5+7 because we know that either D or G = 5, so the correct pair must be 9+3.

But, we have two pairs of numbers that need to add up to 12: B+C and H+I, and only one pair of numbers to acheive it with, therefore our original assumption that D=1 and G=5 must be wrong.

Now assume that D = 5 and G = 1:

We now have 4+B+C+5 = 17, and 1+H+I = 17.

So, B+C = 17-4-5 = 8, and H+I = 17-1 = 16.

Only one pair of numbers add up to make 16: 7+9, so H+ I = 7+9

Of the remaining numbers one pair adds up to 8: 2+6. Therefore B+C = 2+6

We are only left with one other pair: 3+8, so E+F must = 3+8.

If you now plug all these numebers back into the original equations:

4 + 2 + 6 + 5 = 17

5 + 3 + 8 + 1 = 17

1 + 7 + 9 = 17.


Therefore D = 5, and G =1

[Logophobic]

Goodness, was it that simple?

[Harsh Gupta]

yes, it was.

thank you Andy. though i solved it before.

sorry, forgot to mark it resolved.

@Andy, sorry, could not rep you again!!

[Andy_P]

@Andy, sorry, could not rep you again!!

No probs, you can owe me one!