hardlogic

Jack is a farmer and owns some chickens. One day, he took a basket of fresh eggs to the market to sell. The first person bought half of all the eggs in the basket and half an egg. Then, the second person bought half of the remaining eggs and half an egg. Later, the third person bought half of the remaining eggs and half an egg. Now Jack's basket has only 1 egg left. If no eggs were broken in the process, how many eggs did he originally have in his basket?

The answer is 15. The first person bought half of the 15 eggs which is 7½ eggs and another ½ egg. So he bought 8 eggs in total and Jack is left with 7 eggs. The second person bought half of the remaining 7 eggs which is 3½ eggs and another ½ egg. So he bought 4 eggs and Jack is left with 3 eggs. The last person bought half of the remaining 3 eggs which is 1½ eggs and another ½ egg. So the last person bought 2 eggs. That leaves 1 egg remaining in Jack's basket.

Why this works

This riddle cleverly plays with the concept of fractions, making it seem initially confusing but ultimately solvable through logical deduction. Jack's original number of eggs is 15 because, with each sale, the calculations involve taking half of an odd number and adding half an egg. Starting with 15, the first buyer takes 8 eggs (7.5 + 0.5), leaving 7. The second buyer then takes 4 eggs (3.5 + 0.5) from the 7 remaining, leaving 3. Finally, the third buyer takes 2 eggs (1.5 + 0.5) from the 3 left, which results in just 1 egg remaining. The riddle's twist lies in these fractional purchases, making it a fun exercise in arithmetic and logic!

Common Wrong Answers

“12”

If Jack originally had 12 eggs, after the first person bought half (6 eggs) plus half an egg, Jack would have 5.5 eggs left, which cannot be halved again with half an egg, leading to a contradiction.

“10”

Starting with 10 eggs, the first person would buy 5 eggs and half an egg, leaving Jack with 4.5 eggs. This doesn't allow for the second buyer to take half and half an egg properly, resulting in a non-integer count.

“20”

If Jack had 20 eggs, the first buyer would take 10.5 eggs, leaving 9.5 eggs. The second buyer would take 4.75 eggs, leaving 4.75 eggs, which again cannot properly allow for the third buyer to take half and half an egg.

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