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# Puzzles

## Archive

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## 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).

## 19 December

The sum of all the numbers in the eighth row of Pascal's triangle.
Clarification: I am starting the counting of rows from 1, not 0. So (1) is the 1st row, (1 1) is the 2nd row, (1 2 1) is the 3rd row, etc.

## 18 December

The smallest number whose sum of digits is 25.