Coin toss betting having no loss no win puzzle

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Two friends were betting. One said to the other, “The coin will be flipped twenty times and each time the coin lands on head, I will give you $2 and each time it lands on tale, you will give me $3.” After flipping the coin for twenty times not a single penny was exchanged among them.

How many times did the coin land on heads ?coin-toss-bet-puzzle

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  • 2 Answer(s)
    Best answer

    12 Heads and 8 Tails => 12 x 2 = 24 counter-balanced by 8 x 3 = 24.

    Solution: Assume that the coin landed ‘X’ times heads. Since the coin was tossed 20 times, the coin must have landed tails-up  20 – X times.
    Since each ‘Heads’ costs the first person $2, the total due = 2X
    whereas
    his friend would lose $3 for every ‘tails’, adding up to (20 – X) x 3 = 60 – 3X

    Since no money was exchanged,

    2X = 60 – 3X

    => 5X = 60 => X = 12. Hence the result,

    Viji_Pinarayi Expert Answered on 25th October 2016.
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    Let us suppose no of head occurences be x and number of tail ocurrennces will be 20-x ;since total no of throws is20,
    now according to question it is given that for each head  one of the freinds gains $2 so total gain is 2*x.Similarly total loss is 3*(20-x).
    also 2*x=3*(20-x)8
    From the equation x=12.
    Therefore number of heads is 12 and number of tails is 8

    Abhishek Singh Starter Answered on 1st November 2016.
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