(PEEM)base 5 + (PEEM)base 7 = (PEEM)base 8

in this equation each of the letters represents a numer.

Like e is 3 and m is 6 and p is 5.

So what number does "Peem" represent?

Results 1 to 3 of 3

- September 6th 2007, 03:08 PM #1

- Joined
- Sep 2007
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- September 6th 2007, 04:36 PM #2
The setup is

So the problem reads:

Now, we know that P, E, and M are all less than 5 since PEEM is a number in base 5.

So we can start by postulating P = 1:

M is at most 4, so we need E to be at least 3. (And, as it turns out, less than 4.) So try E = 3:

M = 2.

So PEEM = 1332 works.

I can find no other solutions.

-Dan

- October 4th 2007, 03:37 PM #3
Since E and M is

__<__4, 14 E + M is__<__15*4 = 60. Any P__>__2 would make 44 P__>__88, hence the equation doesn't meet in both ends. So P__<__1. P = 0 makes 14 E + M = 0, which only solution is E = M = P = 0.

So PEEM is either 1332 as topsquark pointed out or 0000.