Friday Puzzler -- Coin Flips

Re: Friday Puzzler -- Coin Flips

Re: Friday Puzzler -- Coin Flips

Larry Barrett

The answer is the same if A flips n times and B flips n+1 times, for every value of n.

Correct!

Alex Y

And this may have been what John was alluding to in his no message reply.

Two interesting ways to see this:

Probably the most elegant is that B must have either more heads than A or more tails than A (they are not tied, and with only one more throw, he can't be ahead in both heads and tails) With a fair coin, having more heads or more tails is equally likely.

Another way to look at it is that after each has tossed 99 times, there is an equal probability that A has more heads or B has more heads, along with a non-zero probability that they are tied. If they are tied, there is a 50% chance that B will toss another head. If A has more heads, B will not have more heads even with another toss, while if B is ahead, another toss will not change that.

I could not see either of those when I was presented with this puzzle, even though they seem so obvious once you see them!