The New Sudoku Players' Forum

[rjamil]

A man died. He left three sons as heir; and 17 precious diamonds along with a testament to distribute among them.

According to the father testament, half of the diamonds should go to elder son, one-third should go to middle son and one-nineth should go to youngest son.

His sons were unable to divide the same as the result was coming in fractions.

As the sons were fighting on how to divide among them, a Goldsmith proposed a solution with which all the sons got their share in the property without destroying any diamond.

What was the advice given by the Goldsmith and how the 17 diamonds was divided?

[champagne]

from memory

Hidden Text: Show

borrow one diamond and give it back at the end

[tarek]

Use INT(x)+1. Where x is the fraction of the inheritance

[blue]

The sum of the fractions is 17/18, and 18 is divisible by 2,3 and 9.
Did the goldsmith suggest ?

1st son gets: (18/2) = 9
2nd son gets: (18/3) = 6
3rd son gets: (18/9) = 2

[rjamil]

champagne answer is correct as goldsmith can lend a diamond;
tarek answer also correct subject to a computer program proposed instead of goldsmith; and
blue answer also correct subject to a mathematician proposed instead of goldsmith.

Added:
Being programmer, I recommend CEIL function that rounds up the nearest integer instead of INT(x) + 1.

[tarek]

Added:
Being programmer, I recommend CEIL function that rounds up the nearest integer instead of INT(x) + 1.

For this one specifically the INT was needed because I wanted to the number to be rounded down each time!

Tarek

[SteveG48]

I like the puzzle, but technically as I see it there is no solution. The puzzle calls for each son to get his share of the inheritance, but in fact the solution given results in each son getting more than his share. The father's testament leaves 1/18 of his estate unallocated. (Taxes maybe?) There was nothing left over, so his wishes were not met.

[rjamil]

Hi tarek,

For this one specifically the INT was needed because I wanted to the number to be rounded down each time!

What about, after round-down, adding 1 to get round-up subject to the value always contain fraction part. A single CEIL (x) function takes care about integer value not to add 1.

The father's testament leaves 1/18 of his estate unallocated. (Taxes maybe?) There was nothing left over, so his wishes were not met.

The only issue is to divide 17 diamonds among 3 sons as per father's testament. Rest of the estate/property may be distributed with precision to faction as per estate's current value.

[tarek]

Hi tarek,

For this one specifically the INT was needed because I wanted to the number to be rounded down each time!

What about, after round-down, adding 1 to get round-up subject to the value always contain fraction part. A single CEIL (x) function takes care about integer value not to add 1.

That is correct CEIL(x) in the context of this riddle is enough

tarek

[rjamil]

There is interesting point that youngest son got 1/3, middle son got 2/3 and elder son got 8/9 extra share in diamonds from father's testament calculation point of view.

[blue]

I think you've made a mistake in your math.

The eldest son gets (1/2) diamond extra, the middle son gets (1/3) diamond extra, and the youngest son gets (1/9) diamond extra
... each in proportion to thier original shares, coincidentally.

I still think it's strange that the father wouldn't have specified what was to happen with the remaining (1/18) of his estate.

I think it was to go to the father's mistress, who was also his lawyer ... that there were 18 diamonds originally ... and that the lawyer withheld her share and didn't tell the sons, in fear of an eventual lawsuit

Note: If that was the case, then the sons got exactly what thier father intended (in the way of diamonds, at least) !
Note too: There's still the issue of what to do with the remaining (1/18) of the non-diamond part of his estate.

[tarek]

I’m sure the Goldsmith didn’t Leave empty handed. I suspect that his/her fees would amount to 1/18 of everything

[rjamil]

The eldest son gets (1/2) diamond extra, the middle son gets (1/3) diamond extra, and the youngest son gets (1/9) diamond extra
... each in proportion to thier original shares, coincidentally.

Oops. My mistake.

Note: If that was the case, then the sons got exactly what thier father intended (in the way of diamonds, at least) !

This proofs that the 17 diamonds have been divided into each son as per father's will perfectly.

Eldest son gets 17/2 = 8 1/2;
Middle son gets 17/3 = 5 2/3; and
Youngest son gets 17/9 = 1 8/9.

Note too: There's still the issue of what to do with the remaining (1/18) of the non-diamond part of his estate.

After giving above shares, total 16 1/18 diamonds distributed and there are some fraction of diamond remain, i.e., 17/18, for which it has to be redistributed among sons according to father's will too. And the remaining diamonds are distributed again and again till exhausted.

This puzzle is based on true story and not paradox.
http://www.ezsoftech.com/stories/imamali2.asp

[rjamil]

I got an idea how to show the distribution in simple equation as follows:

Hidden Text: Show

Code: Select all

Lets take each son's share and add them:
17   17   17       1
-- + -- + -- = 16 --
 2    3    9      18

Multiply both the sides of the equation by 18 and divide by 17:
17 × 18   17 × 18   17 × 18   289 × 18
------- + ------- + ------- = --------
 2 × 17    3 × 17    9 × 17    18 × 17

18   18   18
-- + -- + -- = 17
 2    3    9

Hope the above algebraic equation will give exact shares of each son from 17 diamonds as per father's will without dispute.

[SteveG48]

The distribution is correct only if we make assumptions about the father's true intention. Clearly, his testament only distributed 17/18 of his estate. The question is his true intention for the remainder.

If we assume that we should simply multiply each inheritance by the same factor so as to distribute the entire amount, then that factor has to be 18/17. Then the answer already given is exactly correct. The eldest son, for example, gets (9/18)x(18/17) = 9/17. Nine seventeenths of seventeen diamonds is 9. Likewise for the other sons. The puzzle is well formulated to give a nice result. Unfortunately, it requires an assumption. I agree that the mistress should get the extra.