10 Feb '09 10:501 edit

Here's a problem from this year's Intermediate Maths Challenge (a UK competition for, I think, 17 to 18 year olds). They had 25 multiple choice questions to do in an hour. My wife, who is a teacher, did the paper at the same time so that she could answer her pupils' questions afterwards. However she couldn't solve the following one and I felt very pleased with myself when I worked it out in just over a minute.

http://i19.photobucket.com/albums/b177/gallicrow/stacked_squares.jpg

The six stacked squares in this diagram are all equal in size and they are stacked such that there is a vertical line of symmetry.

A straight line is drawn from point A and going through BC such that the total area of the squares and part squares on one side of the line is equal to that on the other side.

Does this line cut BC at:

a) B

b) C

c) 1/3 of the way down BC

d) 1/2 way down BC

e) 2/3 of the way down BC

http://i19.photobucket.com/albums/b177/gallicrow/stacked_squares.jpg

The six stacked squares in this diagram are all equal in size and they are stacked such that there is a vertical line of symmetry.

A straight line is drawn from point A and going through BC such that the total area of the squares and part squares on one side of the line is equal to that on the other side.

Does this line cut BC at:

a) B

b) C

c) 1/3 of the way down BC

d) 1/2 way down BC

e) 2/3 of the way down BC