Place value

problem
Sixty-seven squared

Age

16 to 18

Challenge level

Evaluate these powers of 67. What do you notice? Can you convince someone what the answer would be to (a million sixes followed by a 7) squared?
problem
Three times seven

Age

11 to 14

Challenge level

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
problem
Six times five

Age

11 to 14

Challenge level

How many six digit numbers are there which DO NOT contain a 5?
problem
Just repeat

Age

11 to 14

Challenge level

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?
problem
Which is quicker?

Age

7 to 11

Challenge level

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
problem
Think of two numbers

Age

11 to 14

Challenge level

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
problem
Back to the planet of Vuvv

Age

11 to 14

Challenge level

There are two forms of counting on Vuvv - Zios count in base 3 and Zepts count in base 7. Can you work out in which direction the Zios and Zepts were looking, based on the information you're given?
problem
Reach 100

Age

7 to 11

Challenge level

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
problem
All the digits

Age

7 to 11

Challenge level

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
problem
More mathematical mysteries

Age

11 to 14

Challenge 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 Follow the rest of the instructions then try to explain why this works.