
These problems were kindly supplied by Mr. B Cornish of LRGS Maths Department.
Problem 1
Do unto Caesar . . . . . . .
At Ceasar's palace, Las Vegas, were three poker players  Alan, Bernie and Caroline. At the strat of their night of gambling the amount of money that each one had was in the ratios 7:6:5.
One of the players won $1,200.
What were the asests of the players at the beginning of the evening?
Problem 2
Imagine two cubes. They have integral side lengths (i.e their side lengths are whole numbers, not fractions). Their combined volume is equal to the total length of their edges.
How big are the cubes?
(If you find a result by trial and error then you need to prove that you have found all possible solutions)
Problem 3
Great Granddad is very proud of his telegram from Her Majesty the Queen (and Duke of Lancaster). This congratulates him on his 100th birthday.
He has some friends who are even older than he is.
Great Granddad was born in the year A (where A is the product
of three prime numbers).
Great Granddad was 20 years old in the year B
(where B is the product of a prime number and a square number).
He was 80
years old in the year C (where C is the product of two prime numbers).
He
celebrated his 100th birthday in the year D (where D is even and the product of
four prime numbers.
When was he born?
Problem 4
Problem 5
Link to these problems on the LRGS site.