1
$\begingroup$

The following is a puzzle I found while reading Perfectly Reasonable Deviations from the Beaten Track by Richard P Feynman.

There are 2 shops which sell oranges.At Shop A you get 2 oranges for 5 cents.At Shop B you have to pay 3 cents for each orange.Richard bought some oranges from both the shops.He totally spent 19 cents.How many oranges did Richard buy?How many did he buy from each shop?

Note that Richard did NOT buy 7 oranges.I tried all the conventional methods I know and still ended up with 7 but it's specifically mentioned that the answer is not 7.

Thanks in advance.

  • 0
    It's even "better" if we allow our shopper to buy negative oranges from Shop B. Then you can use the price difference to buy an unbounded number of oranges. E.g. $-7-5k$ oranges from Shop B (leaving him with $19 + (-3)\cdot(-7) + (-3)\cdot(-5k) = 40 + 15k$ cents) and ${40 + 15k \over 5/2} = 16+6k$ oranges from Shop A for a grand total of $9+k$ oranges. [Insert something about silly questions and silly answers here :-)]2011-08-09

1 Answers 1

4

I think you misunderstood what Feynman was saying. If you're referring to the February 29, 1944 letter to his mother: He says that unfortunately he didn't have any problems whose answer was $7$ oranges, and then he makes one up whose answer is $7$ oranges; as far as I can tell he doesn't say anywhere that the answer to this one isn't $7$ oranges.

  • 0
    Well, for reasons too long to get into, I've figured out partially what stuff to retain in an otherwise inconveniently long Google Books URL... :)2011-08-13