this month, Stage 3 & 4

June 1998

 

Problems

problem Icon

Football Sum

Stage:3 Challenge Level:Challenge Level:2Challenge Level:2

Find the values of the nine letters in the sum: FOOT + BALL = GAME

problem Icon

Permute It

Stage:3 Challenge Level:Challenge Level:3Challenge Level:3Challenge Level:3

Take the numbers 1, 2, 3, 4 and 5 and imagine them written down in every possible order to give 5 digit numbers. Find the sum of the resulting numbers.

problem Icon

Quad in Quad

Stage:4 Challenge Level:Challenge Level:1

The points P, Q, R and S are the midpoints of the edges of a convex quadrilateral. What do you notice about the quadrilateral PQRS as the convex quadrilateral changes?

problem Icon

Prime Squares

Stage:4 Challenge Level:Challenge Level:2Challenge Level:2

Every prime number except 2, that is every odd prime number, is the difference of two squares. Prove that there is only one way to express an odd prime number as the difference of two squares. . . .

problem Icon

Fixing the Odds

Stage:4 Challenge Level:Challenge Level:3Challenge Level:3Challenge Level:3

You have two bags, four red balls and four white balls. You must put all the balls in the bags although you are allowed to have one bag empty. How should you distribute the balls between the two. . . .

problem Icon

Xtra

Stage:4 and 5 Challenge Level:Challenge Level:1

Find the sides of an equilateral triangle ABC where a trapezium BCPQ is drawn with BP=CQ=2 , PQ=1 and AP+AQ=sqrt7 . Note: there are 2 possible interpretations.