# Puzzle Nekst 4 2015-2016

**It is summer, so hopefully we are enjoying good weather. In case you wonder what to do all day on a sunny day, Nekst is here to help. Why not crack your brain on this puzzle?**

On a local market in a far-away country, a market stand has fresh fruits for sale. The prices satisfy the following equation:

APPLE = BANANA – LEMON

Furthermore, it is noted that each of the letters in the equation above represents one of the digits from 0 to 9. Each letter represents the same digit in all words, and different letters represent different digits. Assume there are no leading zeros. Determine which digit corresponds to each letter, to find out what the price of an apple is.

Please send your solution to Nekst@Asset-Econometrics.nl before September 16. A crate of beer or a delicious pie, whichever the winner prefers, will be waiting for whoever has the best (partial) solution. Please note that, as before, every recipient of this magazine is eligible to send in their solution, so members of the department are invited to participate as well. Good luck*!*

*Willem Jongen is the winner of the previous puzzle. As a reward, he can come and pick up a crate of beer or a pie at room E1.10. The solution and explanation of the previous puzzle can be found below.
*

## Explanation Puzzle 3 2015-2016

Number the bowls 1 to 10. Take one egg from bowl 1, two eggs from bowl 2,…, ten eggs from bowl 10. Now, suppose that all eggs do indeed weigh ten grams. The total weight will be 550 grams (check for yourself). However, we will never reach this number, because at least one egg is lighter than ten grams. In case bowl 1 was the bowl with the lighter eggs we have one lighter egg, and the total weight is not 550 but 549 grams. Similarly, if bowl 2 was the bowl with the lighter eggs we have two lighter eggs, and the total weight is 548 grams. The same applies to bowls 3 to 10, e.g. if bowl 7 is the bowl with the lighter eggs, we have 7 of those, and the total weight is 543 grams. Concluding, the number of the bowl with the lighter eggs is equal to 550-X, where X is the result of the measurement.

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