Topic Title

[wildrover]

Two gamblers are wagering on coin tosses - one selects heads and one tails. They are playing for £1,000 and first person to get to 10 wins the pot. One of the gamblers is called away with the score Heads 8 Tails 7 and they don't finish the game but they agree to split the pot based on their probability of winning when the game stopped. How should the pot be split?

[wildrover]

As a clue, consider what is the maximum number of coin tosses that can occur before one side or the other must win.

[Stevie C]

Is it £600 to the one on8 & £400 to the other?.

[wildrover]

[JUS]

[wildrover]

[pulse876]

[wildrover]

..is the right answer (11/16 would also have been correct). After 4 rolls someone must win as if Heads hasn't got the 2 Heads he needs then Tails must have got the 3 Tail he needs. There are 16 possible combinations of 4 rolls and they are covered by pulse876's answer as follows:

a) HHHH HHHT HHTH HHTT - Heads wins every time
b) HTHT HTHH THHT THHH - Heads wins every time
c) HTTH THTH HTTT THTT - Heads wins 2 out of 4
d) TTHH TTHT TTTH TTTT - Heads wins 1 out of 4

so overall the probability is that Heads would win 11 times in every 16 and should get £687.50.

[Buzzie]

On a standard 400m running track with semi-circular ends and lanes 1.25m wide, in a 400m race if all the competitors started on the start/finish line instead of being staggered, how much further would the competitor in lane 8 run than the competitor in lane 1?

[wildrover]

I think it's 2 x pi x 7 x 1.25 = 54m 98cm?

[Buzzie]

You would think correctly :D

[wildrover]

Much further than I would have thought - but then again in a 400m race Lane 8 does start more than half way round the bend.

A man is given 4 saplings and told to plant them so that each sapling is the same distance from every other sapling. How did he do it?

[Bigal]

Does the ground have to be flat ?

[JUS]

could you do things with a tetrahedron shaped layout with one planted above the rest?

[wildrover]

Yes - variant on an old favourite. Three are planted in an equilateral triangle around a central mound where the height of the mound is such that the distance from the central sapling to any tree is the same as one side of the triangle.