#119 Nutty neighbours
In Pecan Place, the Shells and the Kernels are staging their annual nut-throwing battle. The Shells have a number of Brazil nuts, while the Kernels have a different number of walnuts.
Suddenly, the Shells throw a fifth of their Brazil nuts at the Kernels, while the Kernels return one-seventh of their walnuts.
After the exchange, the total number of nuts of any kind that the Shells and Kernels possess is now in the ratio 3:5. The total number of nuts is less than 200.
How many nuts did each family begin with?
#118 The spiky shield
Solution
The tightest fit will be found if Alice turns the work diagonally. The distance between the spike tips is 鈭�2 metres (roughly 1.414), as each side is the hypotenuse of a right isosceles triangle with sides of 1 metre.
Alice needs a ratio that is slightly larger than 1.414, but as close to it as possible. A little investigation will reveal that 17/12 metres is slightly larger than 鈭�2 metres, within 3 millimetres of the right length, and the tightest fitting box that Alice will find.
Quick quiz #107
1 Which animal was used as the radio call sign for Russian cosmonaut Valentina Tereshkova while she was in space?
2 The process in which part of Earth鈥檚 crust is folded and deformed by lateral compression to form a mountain range is known as what?
3 Abu al-Qasim Ammar ibn Ali al-Mawsili and Blaise Pascal are both credited with inventing early forms of which device?
4 When were Neanderthal remains recognised as distinct from those of Homo sapiens?
5 Which psychological and evolutionary concept was first formulated by John Bowlby in the 1950s?
Answers
1 A seagull (chaika in Russian)
2 Orogeny
3 The syringe
4 1856
5 Attachment theory