# Thread: Tricky Exponent Problem & Number Sqeuence Problem

1. ## Tricky Exponent Problem & Number Sqeuence Problem

I've been at these problems for HOURS!!!

In the expression below, each letter represents a different digit.

A^5 + B^5 + C^5 + D^5 + E^5 = ABCDE

and

In the array of numbers below, what number should go where the question mark is?
3 11 21 41 91
6 14 15 23 53
3 5 6 8 ?

I would really appriciate any help I can get, thanks very much! (:

2. Originally Posted by Chinchilla Babii
I've been at these problems for HOURS!!!

In the expression below, each letter represents a different digit.

A^5 + B^5 + C^5 + D^5 + E^5 = ABCDE
What have you done so far?

Note: the remainder when divided by 10 of d^5 is d for d=0, 1, ..9

so you have:

A+B+C+D = 0 modulo 10

RonL

3. Originally Posted by Chinchilla Babii
I've been at these problems for HOURS!!!
...

In the array of numbers below, what number should go where the question mark is?
3 11 21 41 91
6 14 15 23 53
3 5 6 8 12

I would really appriciate any help I can get, thanks very much! (:
$\displaystyle \begin{array}{cccccr} 3 & 11&21&41&91& \\ 6 & 14 & 15 & 23 & 53 & \\ 9 & 25 & 36 & 64 & 144 &\text{sum of the columns}\\ 3 & 5 & 6 & 8 & 12 &\text{square-root of the sums}\end{array}$

4. Originally Posted by CaptainBlack
What have you done so far?

Note: the remainder when divided by 10 of d^5 is d for d=0, 1, ..9

so you have:

A+B+C+D = 0 modulo 10

RonL

I wasn't sure if you could use the number ten because it says DIGIT and ten is a two digit number. I've tried 1,2,3,4,5 and 9,8,7,6,5 and other like that but still can't get the answer.

And thank you Earboth, that answer really makes sense. (:

5. 0 0 0 0 0
0 0 0 0 1
0 4 1 5 0
0 4 1 5 1
5 4 7 4 8
9 2 7 2 7
9 3 0 8 4

those are all the possible answers (and only the last has all different digits), but i used a simple program to find them. are you looking for a purely analytical solution?

6. Originally Posted by xifentoozlerix
0 0 0 0 0
0 0 0 0 1
0 4 1 5 0
0 4 1 5 1
5 4 7 4 8
9 2 7 2 7
9 3 0 8 4

those are all the possible answers (and only the last has all different digits), but i used a simple program to find them. are you looking for a purely analytical solution?
Yes, just a purely analytical solution, thanks.

7. oops. I was thinking that when it meant abcde , it meant to multiply A times B times C... etc, Thanks so much!