Can a sum look both ways?
Make 2023 by adding palindromes. Use as few numbers as possible.
The clock starts when you reveal the puzzle.A NUMBER WITH TWO FACES
Read it forwards.
Read it backwards.
One target.
A little symmetry.
MAKE THIS NUMBER
2023
A palindrome reads the same both ways. Single-digit numbers count.AT YOUR OWN PACE
A brain snack, with room to think.
THE ANSWER OPENS ANOTHER DOOR
Now for the lovely part.
You have an answer. Explore how it works, then take the idea somewhere new.
See why it works ↓Keep your time
THE IDEA BEHIND YOUR ANSWER
A reflection.
And a minimum.
Your numbers have matching digits at equal distances from their ends. Inspect the pairs, then see why your sum is as short as it can be.
Read each number in either direction. Its value stays the same.
WHY TWO IS THE MINIMUM
A construction and a limit.
Could one number do it? That number would have to be 2023 itself. But backwards it reads 3202, so it is not a palindrome.
Your answer uses two palindromes and adds to 2023. One is impossible, and two is possible. Together, these facts prove that two is the minimum.
A useful search is to choose a four-digit palindrome, subtract it from 2023, then inspect the remainder. If both numbers read the same backwards, you have a candidate.
The idea to take away
An answer shows what is possible. A lower bound shows how far improvement can go. You often need both to prove something is best.