### 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.

# Chocolate Maths

##### Age 11 to 14Challenge Level

Thank you to Gareth Matthews, Llantwit Major Comprehensive School for this solution. Jenny Cook, age 15, The Mount School York, Andrei Lazanu, age 12, School 205, Bucharest, Romania and Clement Goh, age 13, from River Valley High School, Singapore all sent good solutions.

I used algebra to get my answer.

The problem The solution My calculation
First of all, pick the number of times a week that you eat chocolate. A 7
Multiply this number by 2 (just to be bold). 2A 14
Add 5 (for Sunday). 2A+5 19
Multiply it by 50. 100A+250
This multiplies the original number by 100 and adds 250
950
Add 1750, then the last two digits of the year you last had a birthday. 100A+2000+ab
2709
Now subtract the four digit year that you were born (if you remember). 100A +2000+ab-cdef
Subtracting the year i was born (cdef) from the year I last had a birthday (20ab) gives my age. 100A puts the number A in the hundreds place.
714