Can you select the missing digit(s) to find the largest number?
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
Can you produce convincing arguments that a selection of statements about numbers are true?
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
Can you find out what numbers divide these expressions? Can you prove that they are always divisors?
A polite number can be written as the sum of two or more consecutive positive integers, for example 8+9+10=27 is a polite number. Can you find some more polite, and impolite, numbers?
Can you find a three digit number which is equal to the sum of the hundreds digit, the square of the tens digit and the cube of the units digit?
These secondary problems have not yet been solved. Can you be the first?