Solve for the digits in this Unique set of Palindrome- Pan Digital Expressions:

$2222$ = $(A/B)^C$ + $(D/E)^F$ + $(G/H)^I$

$2222$ = $(A/B)^I$ + $(D/E)^F$ + $(G/H)^C$

Where, A,B,C,D,E,F,G,H,I are distinct digits representing digits 1 to 9.


The solutions are


Explanation (not full and without a proof of uniqueness)

First, find a power of a single-digit integer (with single-digit exponent) slightly less than 2222. Of course, we have $3^7=2187$. The remainder - $2222-2187=35$ can be represented as the sum of 2 powers - $35=2^5+3^1$ in the easiest way. So, we have $2222=3^7+2^5+3^1$. This is a "good" representation of $2222$, since it contains 2 powers of 3, so we can probably find both solutions, and the power bases are small enough (2 and 3) to be represented as the quotient of 2 digits in several ways. Now, arranging the remaining digits to get the desired quotients is trivial task.

| improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.