Geometrical Puzzles

For these puzzles, the solution hinges on goemetry or spatial reasoning. Somtimes a little logic will come in handy, but often you will be left to finding a solution by trial and error.

1. Touching Cigarettes

Arrange 6 cigarettes, so that each is touching the other 5. Then, for a harder challenge, do the same with 7. Your arrangement should be free-standing, and all 7 cigarettes should have a point of contact with each of the other 6.

[ For the purposes of this problem, a cigarette is a perfect (right-circular) cylinder with a length of at least 7 times its diameter. ]

2. From Little Acorns...

Farmer Giles wished to plant 9 new trees in his field. The catch is that when the planting is finished there must be 10 distinct straight lines each containing exactly 3 trees. Can you help him?

3. Match-Makers

Make eight equilateral trianges using just six matches.