this month, Stage 3 & 4

June 1998

 

Problems

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Football Sum

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

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

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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.

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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. . . .

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Quad in Quad (java)

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

ABCD is a convex quadrilateral. The points P, Q, R and S are the midpoints of the edges of ABCD. You can change the shape of the quadrilateral ABCD. What do you notice about the quadrilateral PQRS as. . . .

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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. . . .

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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.