A farmer has a basket of apples. He meets three friends. To the first, he gives half his apples plus half an apple. To the second, he gives half of his remaining apples plus half an apple. To the third, he gives half of his remaining apples plus half an apple. He now has zero apples left and never cut any apple. How many apples did he start with?
7 apples
Work backward: Before the 3rd friend, he had (0 + 0.5) × 2 = 1 apple. Before the 2nd friend, he had (1 + 0.5) × 2 = 3 apples. Before the 1st friend, he had (3 + 0.5) × 2 = 7 apples. At each step, whole numbers of apples were given (4, then 2, then 1).
About this riddle
Logic riddles give you a few facts and ask what must be true. List what you know, cross out what cannot be, and see what is left.
Difficulty: Medium. More like this: Logic riddles with answers or try Einstein's Logic Grid for a different kind of puzzle.
More logic riddles
A row goes: wave, wave, swimmer, wave, wave, swimmer, wave, wave. What comes next?
I am white and floaty, and I can pass through walls. What am I?
A shepherd has sheep that all escape except for nine. Every single one of those remaining sheep runs away, except for six. Then, all of those remaining sheep vanish into the fog, except for four. How many sheep does the shepherd have left?
In a grid of numbers, each row sums to 30. Row 1 has 10, 12, and 8. Row 2 has 15, 5, and X. What is the value of X?
Three runners—Alex, Bea, and Carl—finished a race. Alex was not last. Bea finished immediately before Alex. Who won the race?
Three colored boxes—Red, Blue, and Green—stand in a row. Exactly one box contains a key. The Red Box says: 'The key is in the Blue Box.' The Blue Box says: 'The key is not in this box.' The Green Box says: 'The key is not in the Red Box.' If only ONE statement is true, which box contains the key?