#34 Ant on a tetrahedron
Three short-sighted spiders are clustered at the vertex of a wire frame in the shape of a tetrahedron. The spiders know that there is an ant walking around the frame, but they have no idea where it is. They will only be able to spot it when they are practically on top of it. The ant, on the other hand, has excellent eyesight and can plan its route accordingly to avoid the spiders. Given that the ant walks slightly slower than the spiders, is there a way for the ant to escape the spiders indefinitely? Or can the spiders find a strategy to be certain of catching the ant?
Answer next week
#33 The mountain pass
Solution
The two hikers set off at 6am.
They pass each other at midday after X hours of walking. Bonnie has 4 more hours to go and Aaron has 9. The distance Bonnie has travelled is equal to the distance that Aaron is yet to travel.
Assuming constant walking speeds for both hikers, then the time Bonnie has travelled divided by the time she has left to travel is X/4. For Aaron, the time he has yet to travel divided by the time he has travelled is 9/X.
These two are equal, hence X2=9脳4=36, so X=6.
Quick quiz #32
1 What initially attracts mosquitoes to us?
2 What little green men announced their presence in a field outside Cambridge, UK, on 28 November 1967?
3 On certain dessert wine grapes, the fungus Botrytis cinerea sucks out water to give a sweeter, more intense flavour. What is the mould鈥檚 more PR-friendly name?
4 How many members of the Curie family have won Nobel prizes?
5 Knismesis and gargalesis are two distinct types of what sensation?
Quick quiz #32
Answers
1 Carbon dioxide in our breath. They can smell it up to 50 metres away
2 The first pulsar. LGM-1, or 鈥渓ittle green men 1鈥�, was the playful name given by Jocelyn Bell Burnell to its strangely regular radio signal
3 Noble rot
4 Four: Marie Curie won twice (physics 1903, chemistry 1911), sharing the physics prize with her husband Pierre, and their daughter Ir猫ne Joliot-Curie won jointly with her husband Fr茅d茅ric (chemistry, 1935)
5 Tickle, the light and heavy kinds