Cal Poly Department of Mathematics
Puzzle of the Week
April 10 - 16, 2014
From Dave Camp:
Fibonacci has a puzzle in Liber Abbici which goes as follows: A man whose
end was approaching summoned his sons and said: “Divide my money as I
shall prescribe.” To the eldest son, he said, “You are to have 1 bezant and
a seventh of what is left.” To the second son, he said, “Take 2 bezants and
a seventh of what is left.” To the third son, “You are to take 3 bezants
and a seventh of what is left.” And so he continued with each of his sons:
Each received 1 bezant more than the previous son and a seventh of what
remained, and the last son was to take all that was left. After following
their fathers instructions with care, the sons found that they had shared
their inheritance equally. How many sons were there, and how large was
the estate?
Solutions should be submitted to Morgan Sherman:
Dept. of Mathematics, Cal Poly
Email: sherman1 -AT- calpoly.edu
Office: bldg 25 room 310
before next Thursday. Those with correct and complete solutions will have their
names listed on the puzzle’s web site (see below) as well as in next week’s email
announcement. Anybody is welcome to make a submission.
http://www.calpoly.edu/˜sherman1/puzzleoftheweek
Solution: The estate is 36 bezants and there are 6 sons.
Let E denote the size of the estate, N denote the number of sons, and si the amount son number i receives. First
of all we have:
E−1
E − s1 − 2
s1 = 1 +
, s2 = 2 +
7
7
and equating these gives s1 = 6 so this will have to be the common amount given to each son. Plugging back into
the equation for s1 gives
E−1
6=1+
=⇒ E = 36
7
We also have that E = 6N so we find N = 6. Finally one easily checks that this solution actually fulfills the
requirements of the problem.