# A Mathematical Puzzle Challenge for Archie

OK Archie. I'm going to try to challenge your powers of analysis to
see if you will be able to solve a puzzle. We'll take it one step at
a time. I'll present an instruction and will wait for confirmation
from you before I proceed to the next step. I realize this may drag
the problem out, but it's the only way I can be sure you don't cheat.
Looking at it from your perspective, that's a good thing for you - IF
you are able to provide the solution. Let's begin.

Step 1: Select two three-digit numbers that do not contain any of the
same digits (i.e., you can only use each digit from 0 to 9 one time).
You may use the zero as the leading (first) digit of one of the
numbers, but be sure to keep it on your paper as we will change the
order of the digits in an upcoming step.

Naturally, you should not tell me the numbers you select. Just let me
know when you have two numbers selected.

BTW - I freely admit that I was unable to solve the problem at first
and needed a major hint to get the answer.
.

## Relevant Pages

• Re: Digit Quickie
... of them are powers of a base. ... Now I would break the problem into an exact cover ... of the form {digits of n^e in base b}, ... exponents to use) for the cover. ...
(sci.math)
• Re: MC: 4th power with no small digits
... Let the digits be called "good" and the digits be called ... If you take a collection of fourth powers of a range of integers, ... In other words, what is the sum ... approximations our good, we can expect about 5 solutions. ...
(comp.sys.hp48)
• Re: Can someone please explain - real numbers
... You have to look at it like the computer does, as a string of bits, not a string of decimal digits. ... The 1 bits represent powers of 2 that are included in the sum; the 0 bits represent the powers that are not included. ... As I replied before, the 2.21 value that you store in the Real variable begins as an Extended value, and then the compiler converts it to the best approximation as a Real value. ...
(comp.lang.pascal.delphi.misc)
• Re: Using 2,3,5,7 make 88
... This is quite different from the way I did it, BTW. ... especially when the low number is one of the four digits in the puzzle ... usually by finding a 1 and then raising it to the powers of whatever ...
(rec.puzzles)
• Re: Power of 2 with all even digits?
... An alternative statement of the problem is whether any powers of two ... above 1024 have only digits less than 5 is their base 10 representation. ... the smallest value in the cycle is twice as big. ... If all values in the cycle contain odd digits then once you've reached ...
(sci.math)