Place value

problem
Basically

Age

11 to 14

Challenge level

The number 3723(in base 10) is written as 123 in another base. What is that base?
problem
Tis unique

Age

11 to 14

Challenge level

This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.
problem
Chocolate maths

Age

11 to 14

Challenge level

Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it works?
problem
Two and two

Age

7 to 16

Challenge level

How many solutions can you find to this sum? Each of the different letters stands for a different number.
problem
Which scripts?

Age

7 to 11

Challenge level

There are six numbers written in five different scripts. Can you sort out which is which?
problem
Cayley

Age

11 to 14

Challenge level

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
problem
Oddly

Age

7 to 11

Challenge level

Find the sum of all three-digit numbers each of whose digits is odd.
problem
ABC

Age

7 to 11

Challenge level

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
problem
Quick times

Age

11 to 14

Challenge level

32 x 38 = 30 x 40 + 2 x 8; 34 x 36 = 30 x 40 + 4 x 6; 56 x 54 = 50 x 60 + 6 x 4; 73 x 77 = 70 x 80 + 3 x 7 Verify and generalise if possible.
problem
Never prime

Age

14 to 16

Challenge level

If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.