Puzzle Involving Fractions and a Will left by a Shepherd

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dave1014

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Dear Colleagues,

I have been given the following puzzle involving fractions and don't know where to start: ( I'm afraid I was hopeless at Math's and this is homework for an Adult basic Maths evening class )

An elderly shepherd dies and left his entire estate to his three sons.

The First Son was bequeathed : 1/2 his flock of sheep
The Second Son was bequeathed : 1/3 of his flock of sheep
The Third Son: 1/9 of his flock of sheep.

There are a total of 17 sheep in the estate. How can the sons successfully carry out their fathers wishes?.
 
dave1014 said:
Dear Colleagues,

I have been given the following puzzle involving fractions and don't know where to start: ( I'm afraid I was hopeless at Math's and this is homework for an Adult basic Maths evening class )

An elderly shepherd dies and left his entire estate to his three sons.

The First Son was bequeathed : 1/2 his flock of sheep
The Second Son was bequeathed : 1/3 of his flock of sheep
The Third Son: 1/9 of his flock of sheep.

There are a total of 17 sheep in the estate. How can the sons successfully carry out their fathers wishes?.
Click to expand...
They borrowed one sheep from the neighbor - gave it back after dividing up the rest.....
 
This is a classic, in various forms. Here is one version (in which the problem is reverses, so that you have to find the number 17):

Sam Loyd's Cyclopedia of Puzzles

www.jwstelly.org www.jwstelly.org

You may observe that (in your form, at least) it is more a matter of working around the will, rather than literally carrying it out.
 
1/2+ 1/3+ 1/9= 9/18+ 6/18+ 9/18= 17/18 not 1. That's why they can "borrow" a sheep from a neighbor and the have that sheep left over to give back!
 
HallsofIvy said:
1/2+ 1/3+ 1/9= 9/18+ 6/18+ 9/18= 17/18 not 1. That's why they can "borrow" a sheep from a neighbor and the have that sheep left over to give back!
Click to expand...
And everybody gets more than the bequeathal:

The First Son was bequeathed : 1/2 his flock of sheep ................................................ He gets 9 instead of 17/2
The Second Son was bequeathed : 1/3 of his flock of sheep..................................... He gets 6 instead of 17/3
The Third Son: 1/9 of his flock of sheep. ........................................................................... He gets 2 instead of 17/9
 
Thank you guys.

In working my way through the problem, and trying to find the Lowest Common Denominator for the fractions, I understood the following:
1/2 = 9/18 and 1/3=6/18 but how do you arrive at 1/9 = 9/18 ?. The answer I'm getting is: 1/9= ? /18 and to get the equivalent numerator ( 2 x 9=18), therefore, multiply the numerator and denominator by 2 in 1/9 which becomes 2/18 ?.
I'm not sure how 1/9 becomes 9/18 ?.
 
dave1014 said:
Thank you guys.

In working my way through the problem, and trying to find the Lowest Common Denominator for the fractions, I understood the following:
1/2 = 9/18 and 1/3=6/18 but how do you arrive at 1/9 = 9/18 ?. The answer I'm getting is: 1/9= ? /18 and to get the equivalent numerator ( 2 x 9=18), therefore, multiply the numerator and denominator by 2 in 1/9 which becomes 2/18 ?.
I'm not sure how 1/9 becomes 9/18 ?.
Click to expand...
Halls accidentally typed 9/18 twice, and meant 2/18 for the second. (If you check the sum, you can see that 2 was intended, and this was just a typo.)
 
Thank you Guys for providing the solution.

So far, I'm trying to conceptualize how the solution works - my questions are:

1) A sheep borrowed from a neighbour, makes a total of 18 sheep.

Therefore, 1/2 of 18 sheep = 9
" " 1/3 of 18 sheep= 6
" " 1/9 of 18 sheep = 2

If we then add up 9+6+2 = 17 sheep.
Please bear with me, what I find both interesting and intriguing is why if there are 18 sheep, do the fractions 1/2, 1/3, 1/9 still make the total number of sheep 17?.

2) How does the'extra sheep' borrowed from a neighbour make the solution work ?.

Thank you
 
dave1014 said:
Thank you Guys for providing the solution.

So far, I'm trying to conceptualize how the solution works - my questions are:

1) A sheep borrowed from a neighbour, makes a total of 18 sheep.

Therefore, 1/2 of 18 sheep = 9
" " 1/3 of 18 sheep= 6
" " 1/9 of 18 sheep = 2

If we then add up 9+6+2 = 17 sheep.
Please bear with me, what I find both interesting and intriguing is why if there are 18 sheep, do the fractions 1/2, 1/3, 1/9 still make the total number of sheep 17?.

2) How does the'extra sheep' borrowed from a neighbour make the solution work ?.

Thank you
Click to expand...
The farmer's will was NOT followed exactly. The fractions 1/2, 1/3, 1/9 make

1/2 + 1/3 + 1/9 = 17/18

If we followed the farmer's instructions , exactly - we would have 1/18 sheep left out. Read the previous posts (plural) carefully!!
 
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