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#49 The tree in the snow globe

I have a snow globe that is a hollow hemisphere. At its highest point, it is 10 centimetres tall, and in the centre stands a tree that is 6 cm tall. How far away from the centre can the tree be moved and still stand upright?

Answer next week

#48 Seeing red

Solution

If I see a green traffic light, I should ease off as I will miss the light. If I see a red light, I should accelerate. The actual speed/distance doesn鈥檛 affect the answer, but suppose I am riding at 4 metres per second. The lights are then 60 metres away when I first see them.

If they are green, then I can speed up by at most 25 per cent to 5 m/s, but there is really no point 鈥� I will certainly miss the green light by at least 10 metres. That鈥檚 life, so there is no point in getting upset.

If they are red, then the best strategy is to go at 5 m/s for just 4 seconds. That way I will be 40 metres away, close enough for when the lights change to green. If the lights change during those 4 seconds when I have bothered to speed up, then I will be 鈥渞eally upset鈥� because I am still too far away. The total lights sequence takes 100 seconds, so on average, that is going to happen on 4 per cent of my journeys.

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