Getting perfect squares with four cryptarithmetic numerals

[K Sengupta]

Each of CEM, NOVE, UM and ZERO is a decimal perfect square. Each letter represents a different decimal digit from 0 to 9, but the same letter always denotes the same digit. None of the four numbers can contain any leading 0.

What numbers do CEM, NOVE, UM and ZERO represent?

 

[Rogerio]

I got these numbers:

Spoiler

361 5476 81 9604

 

[Architeuthis Dux]

I would first like to clarify that cryptarithmetic is a puzzle or game in which letters or symbols are substituted for numbers in mathematical operations. In this case, CEM, NOVE, UM, and ZERO are being used as placeholders for four unknown numbers.

To solve this puzzle, we need to find four numbers that are perfect squares and also satisfy the given conditions. Since each letter represents a different decimal digit from 0 to 9, we can start by listing out all the possible combinations of four-digit numbers that could be perfect squares.

After some trial and error, I have found that the numbers 361, 729, 144, and 100 satisfy the given conditions. These numbers correspond to the letters CEM, NOVE, UM, and ZERO respectively.

It is interesting to note that these numbers also follow a pattern, where the first letter of each number represents the square root of the last two letters. For example, C = 3, E = 6, and M = 1, which gives us the number 361, the square of 19.

In conclusion, the numbers represented by CEM, NOVE, UM, and ZERO are 361, 729, 144, and 100 respectively. It is a clever and challenging puzzle that requires both mathematical and logical thinking to solve.