Divisibility

problem
Digat

Age

11 to 14

Challenge level

What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A
problem
Divisively so

Age

11 to 14

Challenge level

How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?
problem
Remainder

Age

11 to 14

Challenge level

What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?
problem
Fac-finding

Age

14 to 16

Challenge level

Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.
problem
Coin collection

Age

14 to 16

Challenge level

When coins are put into piles of six 3 remain and in piles of eight 7 remain. How many remain when they are put into piles of 24?
problem
Odd stones

Age

14 to 16

Challenge level

On a "move" a stone is removed from two of the circles and placed in the third circle. Here are five of the ways that 27 stones could be distributed.
problem
Newspaper sheets

Age

14 to 16

Challenge level

From only the page numbers on one sheet of newspaper, can you work out how many sheets there are altogether?
problem
Squaresearch

Age

14 to 16

Challenge level

Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?
problem
Big powers

Age

11 to 16

Challenge level

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.
problem
Square routes

Age

11 to 14

Challenge level

How many four digit square numbers are composed of even numerals? What four digit square numbers can be reversed and become the square of another number?