Ten Problems

Have you heard of the Four Squares Theorem? It states that every non-negative integer can be expressed as the sum of four squares.

Complete the following equality:

SQUARE + SQUARE + SQUARE + SQUARE = NUMBER

Replace the following letters with digits to satisfy the equation.

SPAM+SPAM+SPAM+SPAM+SPAM+SPAM=EMAIL

Since this is quite a tough problem, I’m not going to post nine more problems today, and I hope everyone try this because it is actually really interesting.

Replace the letters and asterisks with digits to satisfy the multiplication:

Don’t ask me what “Estmodus Inrebus” means. I have no clue. FYI this puzzle comes from “The Master Book of Mathematical Recreations” created by a mathematician by the name of Fred Schuh. I’ll try to post a full solution to this problem in a few days.

Edit: I just found out what the phrase means. It’s actually “Est modus in rebus”, a quote from Horace (Ancient Roman poet), meaning “There is a measure in things”.

Update: The complete solution is posted!

Restore the following equation:

EVE/DID = 0.TALKTALKTALK…

where each letter represents a digit.

Here is another interesting ‘restore the equation’ type problem. It was first asked by a New York math prof Alan Wayne who published it in the 1947 August issue of American Mathematical Monthly.