## Teaser 2897: Easter egg

**From The Sunday Times, 1st April 2018** [link]

“Granddad, I’ve got a great big Easter egg in a square box!” My grandson Liam inspired this Teaser in which I have used non-zero digits then consistently replaced them with letters, using different letters for different digits.

In this way, I have:

EASTER

(EGG)²

BOXTwo of the numbers add to make the third, and if I told you which number was largest you should be able to solve this Teaser.

Find the value of

BOX.

[teaser2897]

## Jim Randell 8:52 am

on22 July 2019 Permalink |EASTERhas 6 digits,(EGG)²has 5 or 6 digits, but whichever is largerBOXis the difference between them.The alphametic expression:

only has one solution (when we don’t use the digit 0):

So this gives us our solution (

BOX=362), even without needing to know which ofEASTERor (EGG)² is larger. (In factEASTER>(EGG)²).But here is a full solution, that solves the two possible sums as alphametic problems, and looks for situations where there is a single solution for

BOX. It runs in 122ms.Run:[ @repl.it ]Solution:BOX = 362.In fact this program runs faster than the single alphametic expression above, as each alphametic expression only requires considering the possibilities for 5 digits, rather than 6 with the single sum.

If (non-leading) 0 digits are allowed, then there are three further solutions to the

(EGG)² + BOX = EASTERsum (but still none for(EGG)² – BOX = EASTER).LikeLike

## GeoffR 8:52 am

on30 July 2019 Permalink |LikeLike