Puzzle – How many Chickens were sold by the farmer?
A farmer bought chickens for 4 unique clients on a selected day. Each customer buys half the amount of chicken left till his turn and half a chicken (i.e., if x chicken were left he buys x/2 + 1/2). The fourth customer buys a single chicken and after his turn, no chicken was left. Can you find the number of chickens the farmer bought on that day?
Answer:
Let, the customers are C1, C2, C3, and C4 and the Number of chickens is X.
Customer 1: The first customer will buy (X/2 + 1/2) chicken and the left amount will be X – (X/2 + 1/2) = (X – 1)/2.
Customer 2: The amount of chicken the second customer will buy is (X-1)/4 + 1/2 = (X+1)/4. So the amount of chicken left will be
(X – 1)/2 – (X + 1)/4 = (X-3)/4.
Customer 3: The amount of chicken bought by the third customer will be ((X-3)/4)/2 + 1/2 = (X-3)/8 + 1/2 = (X+1)/8. So the remaining amount of chicken is (X – 3)/4 – (X + 1)/8 = (X – 7)/8.
Customer 4: The amount of chicken bought by the fourth customer is ((X-7)/8)/2 + 1/2 = (X – 7)/16 + 1/2 = (X + 1)/16. The amount of chicken left is (X – 7)/8 – (X + 1)/16 = (X – 15)/16.
Given that the fourth customer purchased only single chicken and no chicken is left after his purchase:
(X – 15)/16 = 0
So X – 15 = 0
X = 15
Therefore, the farmer sold 15 chickens on that particular day to each customer as follows,
Customer 1: C1 = (15 + 1)/2 = 8 Chickens
Customer 2: C2 = (15 + 1)4 = 4Chickens
Customer 3: C3 = (15 + 1)/8 = 2 Chickens
Customer 4: C4 = (15 + 1)/16 = 1 Chicken
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