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?
How many Chickens were sold by the farmer?
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.
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Chicken sold to first customer
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.
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Chicken sold to Customer 2
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.
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Chicken sold to Customer 3
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.
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Chicken sold to Customer 4
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
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?
How many Chickens were sold by the farmer?
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.
Chicken sold to first customer
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.
Chicken sold to Customer 2
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.
Chicken sold to Customer 3
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.
Chicken sold to Customer 4
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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