### Double Digit

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. Try lots of examples. What happens? Can you explain it?

### Repeaters

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

### Big Powers

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

# More Mathematical Mysteries

##### Age 11 to 14Challenge Level

Write down a three-digit number

Change the order of the digits to get a different number

Find the difference between the two three digit numbers

Add together the digits of your answer. If you arrive at a two-digit answer, add the two digits to reduce your answer to a single digit answer

Subtract $5$ from the number you have

Find that equivalent number letter in the alphabet (1=A, 2=B etc.)

Name a country that begins with letter

Using the second letter of the name of the country that you chose, name a jungle animal that starts with that letter.

Name the colour of that animal.

Using the final letter of the name of the country that you chose, name a different animal that starts with that letter.

Name a fruit that starts with the last letter of that animal's name.

Did you end up with orange or apple?

How did I know?