## October 2017 Logic & Maths Problems – Solutions

1. 24
For 5 teams to play each other twice requires 20 games to be played.
If either of the two top teams then has 4 straight wins, no further games are required.

2. 720 – 24 = 696

3. The SOLIDUS. You may see the answer as VINCULUM in some places but the word vinculum is a more general term referring to any horizontal line used in mathematical representation, including (for example) the line above a recurring decimal.

4. 30%

5. 13

6. 24 hours
The energetic gardener can mow the lawn in 12 hours. He can therefore mow 1/12 of the lawn in one hour, so his contribution to mowing the whole lawn in 8 hours is 8/12 or 2/3 of the lawn mowed.
In 8 hours the lazy gardener has therefore mowed the remaining 1/3 of the lawn. He is therefore mowing at the rate of 1/24 of the lawn per hour. It would take him 24 hours to mow the entire lawn by himself.

7. Mr Blue – red shirt Mr White – blue shirt Mr Red – white shirt

8. (a) Guy Sebastian (b) Neil Young (c) Ringo Starr

9. 126 (and that’s the unvarnished truth.)
All the surface cubes will have varnish on them. There will be
(9 – 2) × (8 – 2) × (5 – 2) = 7 × 6 × 3 cubes = 126 which are not on the surface.

10. Left to right: jack of clubs, jack of diamonds, queen of diamonds.