Rhind Papyrus 100 Loaves 5 Men Puzzle - Solution
The Puzzle:
100 loaves of bread must be divided among five workers.
Each worker in line must get more than the previous: the same amount more in each case (an arithmetical progression).
And the first two workers shall get seven times less than the three others.
How many loaves (including fractions of a loaf!) does each worker get?
Our Solution:Let us say the middle worker (worker 3) gets "w" loaves.
And that "d" is the common difference between workers.
So the workers get:
w-2d
w-d
w
w+d
w+2d
The middle worker gets a perfect average, so 100/5 = 20 loaves
The first two workers get seven times less than the three others:
7*[(20-2d) + (20-d)] = 20 + (20+d) + (20+2d)
From this: d = 220/24, or 55/6
And this is the solution:
1st worker = 10/6 loaves
2nd worker = 65/6 loaves
3rd worker = 120/6 (20) loaves
4th worker = 175/6 loaves
5th worker = 230/6 loaves
And that "d" is the common difference between workers.
So the workers get:
w-2d
w-d
w
w+d
w+2d
The middle worker gets a perfect average, so 100/5 = 20 loaves
The first two workers get seven times less than the three others:
7*[(20-2d) + (20-d)] = 20 + (20+d) + (20+2d)
From this: d = 220/24, or 55/6
And this is the solution:
1st worker = 10/6 loaves
2nd worker = 65/6 loaves
3rd worker = 120/6 (20) loaves
4th worker = 175/6 loaves
5th worker = 230/6 loaves