[chelseapendley]

When Mattie went to college, she was assigned a password to use on the computer system. The password consisted of a series of five different digits. She was told to memorize it and not write it down.

Mattie decided to invent a reminder, but all she could come up with was:
(1) The sum of the first two digits was exactly twice the sum of the last four.

And

(2) The sum of the three digits in the middle was twice the sum of the last two.

On the first day of classes, Mattie forgot her password. From her reminder, can you reconstruct the password?

[ebaines]

Try setting up a couple of equations. Let A = 1st digit, B = 2nd digit , etc, and you get these two equations from the data you provided:

(1) A+B = 2(B+C+D+E)
(2) B+C+D = 2(D+E)

From (1) you can rearrange to get: A = B+2C+2D+2E. You know that A must be 9 or less (since it's a single digit); from that you can see that C, D and E must be 0, 1, and 2 (not necessarily in that order), because any other valiues would make A >9. So now you have A = B + 2 (0+1+2) = B+6. For A to be 9 or less that means B must be 3, and therefore A = 9.

Now you just need to try different combinations of 1, 2,3 for C, D and E to make equatoin (2) work.

[chelseapendley]

So is the answer 93102?

[ebaines]

so is the answer 93102?

It certainly sems to fit the criteria - so that must be it!

[chelseapendley]

Thanks..