Mathematical_Recreations-Kraitchik-2e

34 Mathematical Recreations
apples of identical quality, so they had to keep their prices
equal. At the end of the day Mr. Pappas had sold 10 apples,
Mr. Gatta 25, and Mrs. Murphy 30, yet all had taken in the
same total. How much did they charge, and how much did
they take in? (After Ozanam, 1741)
Answer: The problem is possible only if the price was
changed in the course of the day. Assuming just one price
change, these are the ten possible basic solutions:
Solution
No.
Dealer
Sales at first Sales at second
price price Total, each
dealer,
"" >=: "" >=:
:::l :::l
No. Price, No. Price, cents
0 0
sold cents
~
sold cents S
<
--------
Pappas 4 24 6 6
1 Gatta 1 6 6 24 1 24 30
Murphy 0 0 30 30
----------
Pappas 5 30 5 5
2 Gatta 2 6 12 23 1 23 35
Murphy 1 6 29 29
----------
Pappas 6 36 4 4
3 Gatta 3 6 18 22 1 22 40
Murphy 2 12 28
--------
28
Pappas 7 42 3 3
4 Gatta 4 6 24 21 1 21 45
Murphy 3 18 27
--------
27
Pappas 8 48 2 2
5 Gatta 5 6 30 20 1 20 50
Murphy 4 24 26 26
----------
Pappas 9 54 1 1
6 Gatta 6 6 36 19 1 19 55
Murphy 5 30 25 25