Place value

problem

Song Book

Age

7 to 11

Challenge level

A school song book contains 700 songs. The numbers of the songs are displayed by combining special small single-digit cards. What is the minimum number of small cards that is needed?
game

Nice or Nasty for Two

Age

7 to 14

Challenge level

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
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

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

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

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.
problem

Not a Polite Question

Age

11 to 14

Challenge level

When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...
problem

Writ Large

Age

11 to 14

Challenge level

Suppose you had to begin the never ending task of writing out the natural numbers: 1, 2, 3, 4, 5.... and so on. What would be the 1000th digit you would write down.
problem

Eleven

Age

11 to 14

Challenge level

Replace each letter with a digit to make this addition correct.
problem

Back of the Queue

Age

11 to 14

Challenge level

Weekly Problem 48 - 2013
What is the remainder when the number 743589 × 301647 is divided by 5?