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# Puzzles

## Archive

Show me a Random Puzzle
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## 11 December

Two more than today's number is the reverse of two times today's number.

## 4 December

Pick a three digit number whose digits are all different.
Sort the digits into ascending and descending order to form two new numbers. Find the difference between these numbers.
Repeat this process until the number stops changing. The final result is today's number.

## 1 December

Today's number is the smallest three digit number such that the sum of its digits is equal to the product of its digits.

## XYZ

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

## 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?

## 18 December

The smallest number whose sum of digits is 25.

## 10 December

The smallest number that is equal to the sum of its digits multiplied by ten more than the sum of its digits.

## 6 December

When you add up the digits of a number, the result is called the digital sum.
How many different digital sums do the numbers from 1 to 1091 have?*
* There was a mistake in this question (it previously said 1092). If you answered the typo'd question right, your answer should automatically correct itself to 9 less than it was...
© Matthew Scroggs 2018