# Euler’s Riddle

Please comment your solutions, questions and remarks..

I found in a recreational book the following riddle attributed to Leonard Euler. The book gives a clumsy solution involving solutions of quadratic equations, a lot of fractions and half a page of text. I challenge you to find an elegant solution! (I am sure elegance was Euler’s intension!),

Euler’s riddle: Two traders went to a market to sell eggs. Each of them had her own eggs and they had 100 eggs altogether. After selling all their eggs they earned the same amount of money. One of them says to the other: If I had as many eggs as you had, I would have earned 15 Kreuzers. Then the other replies: If I had as many eggs as you had, then I would have earned $$6\frac{2}{3}$$ Kreuzers. How many eggs did each of them bring?

Level 1/5 for a solution, 2/5 for an elegant one, 3/5 for a solution more elegant than that I have in mind.

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### 2 Responses to Euler’s Riddle

1. KP says:

Answer 40 and 60 eggs.

Suppose first trader sells at cost c1 and 2nd trader sells at cost c2. Let first trader have x eggs. then th eother one has (100 – x) eggs.

So we have

x*c1 = y –(1)
(100-x)*c2 =y –(2)
(100 – x)*c1 = 15 –(3)
x*c2 = 20/3 –(4)

(3)/(4) gives ((100-x)/x) * (c1/c2) = 9/4
but (2)/(1) gives (100-x)/x = c1/c2

so (100 -x)/x are in the ratio 3:2. Divide 100 in the ratio 3:2 we are done

2. I think this is just above 2 points :) Thank you.