## August 2017 Logic & Maths Problems – Solutions

1. 18

2. Daniel is 7, Jessica is 4

3. 32
They change square colour when they move. So if they were all on the 32 white squares or the 32 black squares they could not attack each other.

4. 102 pages
To eat 300 pages with the books stacked as shown, the bookworm would have to eat from p100 Vol 1 to p1 vol 3

5. The red door
Process of elimination as follows:

6. a. 13; b. 18; c. 3

7. a

8. a. Keith b. first c. Adrian

9. 2/3 (not 1/2)

You know that you do not have Bag B (two black marbles) so there are three possibilities

You chose Bag A, first white marble. The other marble will be white
You chose Bag A, second white marble. The other marble will be white
You chose Bag C, the white marble. The other marble will be black

So 2 out of 3 possibilities are white.

Why not 1/2? You are selecting marbles, not bags.

10. 125 m3..

(half as high means all three dimensions are in the ratio 0.5.

The smaller pyramid’s volume is

0.5 × 0.5 × 0.5 = 0.125

` that of the larger pyramid.)`