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# Puzzles

## Archive

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## XYZ

Which digits $$X$$, $$Y$$ and $$Z$$ fill this sum?
$$\begin{array}{cccc} &X&Z&Y\\ +&X&Y&Z\\ \hline &Y&Z&X \end{array}$$

## Where is Evariste?

Evariste is standing in a rectangular formation, in which everyone is lined up in rows and columns. There are 175 people in all the rows in front of Evariste and 400 in the rows behind him. There are 312 in the columns to his left and 264 in the columns to his right.
In which row and column is Evariste standing?
Tags: numbers

## Elastic Numbers

Throughout this puzzle, expressions like $$AB$$ will represent the digits of a number, not $$A$$ multiplied by $$B$$.
A two-digit number $$AB$$ is called elastic if:
1. $$A$$ and $$B$$ are both non-zero.
2. The numbers $$A0B$$, $$A00B$$, $$A000B$$, ... are all divisible by $$AB$$.
There are three elastic numbers. Can you find them?

## Square Pairs

Source: Maths Jam
Can you order the integers 1 to 16 so that every pair of adjacent numbers adds to a square number?
For which other numbers $$n$$ is it possible to order the integers 1 to $$n$$ in such a way?

## Factorial Pattern

$$1\times1!=2!-1$$ $$1\times1!+2\times2!=3!-1$$ $$1\times1!+2\times2!+3\times3!=4!-1$$
Does this pattern continue?

## 24 December

Today's number is 191 more than one of the other answers and 100 less than another of the answers.
Tags: numbers

## 23 December

Today's number is the number of three digit numbers that are not three more than a multiple of 7.
Tags: numbers

## 22 December

Today's number is a palindrome. Today's number is also the number of palindromes between 111 and 11111 (including 111 and 11111).