# 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 ? 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,

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