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.

Quick Times

Age 11 to 14Challenge Level

$32 \times 38 = 30 \times 40 + 2 \times 8$

$34 \times 36 = 30 \times 40 + 4 \times 6$

$56 \times 54 = 50 \times 60 + 6 \times 4$

$73 \times77 = 70 \times80 + 3 \times 7$

And so on?

Verify and generalise if possible.