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Sunday, January 6, 2008

Shingles and Apples

There is an old story of a trader who put into Philadelphia with a boat load of shingles, some of which had been damaged in passage. He was asked by a Quaker merchant what the price was for the shingles.

"They are $10 a bundle," he replied, "if you choose the the bundles and $5 a bundle if I choose them."

The merchant thought for a minute and said, "Captain, I will buy your whole cargo, and you may choose the bundles."

The following puzzle involves a similar principle:

A man had an apple stand and sold his larger apples at three for a dollar and his smaller apples at five for a dollar. When he had just thirty apples of each size left to sell, he asked his son to watch the stand while he had lunch. When he came back from lunch the apples were all gone and the son gave his father $15. The father questioned his son.

"You should have received $10 for the thirty large apples and $6 for the thirty small apples, making $16 dollars in all."

The son looked surprised. "I am sure I gave you all the money I received and I counted the change most carefully. It was difficult to manage without you here, and as there were an equal number of each sized apple left, I sold them all at the average price of four for $1. Four goes into sixty fifteen times so I am sure $15 is correct."

Where did the missing $1 go?


Unknown said...

You can read an explanation of the missing dollar here:

Anonymous said...

The "Shingles and Apples" puzzle is not really a puzzle. The apples were sold at different prices and thus there is a difference in the returns.

In short, there is no missing dollar.

Here is why:

3 large apples @ $1
5 small apples @ $1

30 large and 30 small apples

30/3 = $10
30/5 = $6
$10 + $6 = $16 -> this is what the father expects

The son sold the apples at $1 per 4 apples:

4 apples @ $1

60/4 = $15 -> this is what the son sells

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This is a fun site but I cannot find answers to a lot of puzzles other than reading the comments if any. I wish the authors would post solutions.