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        riddles >> medium >> Inheritance problem
        
(Message started by: mikedagr8 on Aug 30th, 2007, 2:59am)
Title: Inheritance problem
Post by mikedagr8 on Aug 30th, 2007, 2:59am
A father leaves his seven sons $14148167 as an inheritance, and the rest to charity. In his will he makes a proviso that everything must be given to charity if the sons cannot divide the money equally between them. So they can't give x dollars away and then divide up, it must all be divided equally as it is currently. Is there a way in which they can inherit?
Title: Re: Inheritance problem
Post by towr on Aug 30th, 2007, 4:18am
[hide]Convert it to gold, divide the gold equally?

Or redefine what "equally" means :P[/hide]
Title: Re: Inheritance problem
Post by mikedagr8 on Aug 30th, 2007, 4:24am
Equally means that they all recieve the exact same amount of money. So not repeating decimals of a cent value. We want it so that there is none of that and everything is equal. Gold is not allowed as the inheritance came in $.

This is a real toughy I found.

Think laterally and be very open minded.
Title: Re: Inheritance problem
Post by pex on Aug 30th, 2007, 4:29am
[hide]Give $2021166 to each and cut the remaining bills so that each can get 5/7 of them?[/hide]
Title: Re: Inheritance problem
Post by towr on Aug 30th, 2007, 4:33am
Burn it and divide the ash.
Title: Re: Inheritance problem
Post by mikedagr8 on Aug 30th, 2007, 4:35am
Nope, they all get an equal amount and no money is left as the remainder. Like when cutting up bills, becuase then there value is 0.

P.S. This is a really silly puzzle, I wouldn't be surprised if no one got it.
Title: Re: Inheritance problem
Post by pex on Aug 30th, 2007, 4:37am

on 08/30/07 at 04:35:03, mikedagr8 wrote:
This is a really silly ouzzle, I wouldn't be surprised if no one got it.

Okay... maybe [hide]some currency existed, or still exists, which is called a dollar and has 1/7 dollar coins, enough of which happened to be present in the inheritance[/hide]?
Title: Re: Inheritance problem
Post by mikedagr8 on Aug 30th, 2007, 4:42am
Nope. This is in a normal currency. So lets say American dollars.
Title: Re: Inheritance problem
Post by SMQ on Aug 30th, 2007, 4:53am
One of the brothers has an idea: [hide]he gets together with four of the others, and together they plot to murder the remaining two brothers.  Now each of the surviving five brothers gets $2829633.40[/hide]

Or

They [hide]hire an attorney to solve the problem for them.  After some thought he charges $148,167 as a fee and splits the remaining $14,000,000 evenly among the brothers.[/hide]

--SMQ
Title: Re: Inheritance problem
Post by towr on Aug 30th, 2007, 5:01am
co-ownership seems equal enough.
They can divide all but 15 dollars normally, and from the co-owned 15 dollar they buy a cake to celebrate their solution to the problem.
Title: Re: Inheritance problem
Post by mikedagr8 on Aug 30th, 2007, 5:04am
No to all.
Title: Re: Inheritance problem
Post by towr on Aug 30th, 2007, 5:10am
Are there any daughters that should also get a share but sneakily went unmentioned?
Title: Re: Inheritance problem
Post by mikedagr8 on Aug 30th, 2007, 5:12am
No daughters. Only seven benifactors. By normal currency I mean that once you solve the puzzle, you will see how it is normal. Until then Good Luck.

If will this puzzle continues for a few days with no correct answer, I will give some major clues.
Title: Re: Inheritance problem
Post by pex on Aug 30th, 2007, 5:28am
The sons set up a charity organization.
Title: Re: Inheritance problem
Post by SMQ on Aug 30th, 2007, 5:34am
Six of the brothers receive $1,286,197 in $1 bills, while the seventh brother receives $6,430,985 in $5 bills.  Every brother has the same number of bills, and so the same "amount" of money.

--SMQ
Title: Re: Inheritance problem
Post by mikedagr8 on Aug 30th, 2007, 5:39am
That's brilliant. But no, They also need to have the same value. I love that though. Kudos.
Title: Re: Inheritance problem
Post by Grimbal on Aug 30th, 2007, 5:59am
They pay 10% inheritance tax, or $1414817 (rounded).
The rest is split and everybody receives $1819050
Title: Re: Inheritance problem
Post by Aryabhatta on Aug 30th, 2007, 1:47pm
They go to the nearest foreign exchance bank and convert it some other suitable currency (say euro) and then split it up.

The cost of conversion, they split up equally from their share, after they get the amounts.
Title: Re: Inheritance problem
Post by mikedagr8 on Aug 30th, 2007, 3:03pm
Nope.
Title: Re: Inheritance problem
Post by srn347 on Aug 31st, 2007, 9:34pm
They convert into foreign money, wait for the value to change, convert back to american money, and divide it.
Title: Re: Inheritance problem
Post by mikedagr8 on Sep 1st, 2007, 2:22am
Not even close. One more day and I will help you all out.
Title: Re: Inheritance problem
Post by denis on Sep 1st, 2007, 5:00am
Just give them each a check for 202116 and 5/7 dollars.

On your standard checks you have two sections: the dollars then the /100 section for cents.

So you would have for example seven Dollars and 34/100 to represent 7.34

This 1/100 is the part that does not divide well and we need to change.

Since a check is a contract it can be written in any way. So what you do is cut them each a check for 202116 and 5/7 dollars.  Furthermore, this check represents the exact value of the inheritance required so you are done. What the bank does when it deposits into each benefactor's account (round up or round down) does not really concern us because no US bank or currency in us dollars can actually split the inheritance exactly in 7 equal portions.
Title: Re: Inheritance problem
Post by mikedagr8 on Sep 1st, 2007, 5:04am

on 09/01/07 at 05:00:32, denis wrote:
Just give them each a check for 202116 and 5/7 dollars.

On your standard checks you have two sections: the dollars then the /100 section for cents.

So you would have for example seven Dollars and 34/100 to represent 7.34

This 1/100 is the part that does not divide well and we need to change.

What you do is cut them each a check for 202116 and 5/7 dollars. Since a check is a contract it can be written in this way. Furthermore, this check represents the exact value of the inheritance required so you are done. What the bank does when it deposits into each benefactor's account (round up or round down) does not really concern us.



Yes, I was thinking that as well when I saw the puzzle, Although it is technically correct, the puzzle was not designed for that answer. Well done though.

Keep guessing everyone, the answer is still out there.
Title: Re: Inheritance problem
Post by srn347 on Sep 1st, 2007, 9:42am
They fight to the death until enough people are dead that the living people can divide it evenly.
Title: Re: Inheritance problem
Post by Eigenray on Sep 1st, 2007, 12:26pm
One brother gets $2021171, and the other 6 each get $2021166 plus an IOU for the present value of $5/7.  At some point in the future, the IOU will be worth an integral number of pennies, so they can settle their debts then (assuming they agree on the time value of money).

A similar solution is to open an interest bearing account and wait for the balance to be a multiple of 7 cents.
Title: Re: Inheritance problem
Post by mikedagr8 on Sep 1st, 2007, 4:15pm
Rofl, no, it gets divided evenly, I assure you.

First clue: There is no cent value in what they each recieve. E.g. they may recieve $5.00 (this is not the correct answer, only a clue). Worded better, they recieve whole dollars. I hope that's clearer now.
Title: Re: Inheritance problem
Post by mikedagr8 on Sep 3rd, 2007, 1:06am
I'm going to assume no one answered because they still have no idea of how they can do it.

Second Clue: They all recieve a multiple of $10,000.
Title: Re: Inheritance problem
Post by towr on Sep 3rd, 2007, 1:42am
Then what happens to the remaining $8167?
It seems to violate the premise of the riddle..
Title: Re: Inheritance problem
Post by mikedagr8 on Sep 3rd, 2007, 1:44am
No, not when I give you the next 2 clues it wont.
Keep guessing though, I found this puzzle very dubious, took me several hours until I reached the answer that was given. You guys are approaching it, but not quite getting there.
Title: Re: Inheritance problem
Post by pex on Sep 3rd, 2007, 2:25am
Aha! Maybe $14148167 is [hide]not supposed to be read as a decimal number, but rather in some other number base that makes it divisible by seven?[/hide]
Title: Re: Inheritance problem
Post by mikedagr8 on Sep 3rd, 2007, 2:28am

on 09/03/07 at 02:25:50, pex wrote:
Aha! Maybe $14148167 is [hide]not supposed to be read as a decimal number, but rather in some other number base that makes it divisible by seven?[/hide]


Bingo!!! What base?   :D
Title: Re: Inheritance problem
Post by pex on Sep 3rd, 2007, 2:45am

on 09/03/07 at 02:28:28, mikedagr8 wrote:
Bingo!!! What base?   :D

Any base greater than eight and equal to 0 or 1 (mod 7). Thus, 14, 15, 21, 22, 28, 29, 35, 36, ...

The multiple of $10000 thing is not yet working for me.
Title: Re: Inheritance problem
Post by mikedagr8 on Sep 3rd, 2007, 2:47am
ROFL!!! Well, still not quite there yet. Oh to make things more fun, you have to convert it back into a base. I'm not telling you which. This clue is deceptive, so believe what you want.
Title: Re: Inheritance problem
Post by Barukh on Sep 3rd, 2007, 2:49am

on 09/03/07 at 02:45:39, pex wrote:
Any base greater than eight and equal to 0 or 1 (mod 7). Thus, 14, 15, 21, 22, 28, 29, 35, 36, ...

Why? I agree only wtih a half of these.

Besides, I think you missed a few.


Quote:
The multiple of $10000 thing is not yet working for me.

[hide]9[/hide]
Title: Re: Inheritance problem
Post by mikedagr8 on Sep 3rd, 2007, 2:51am
And Barukh wins  :D!!! Sorry Pex, I sent you a message to help you, but Barukh got there first  :(. Well done picking up the loose ends. What you think of the puzzle guys?

For those who cared, the next two clues were they each recieve $1,000,000 and this is not in base 10.
Title: Re: Inheritance problem
Post by Barukh on Sep 3rd, 2007, 2:53am

on 09/03/07 at 02:51:14, mikedagr8 wrote:
And Barukh wins  :D!!! Sorry Pex, I sent you a message to help you, but Barukh got there first  :(.

All the credit goes to pex.


Quote:
What you think of the puzzle guys?

I really liked this one!

:D
Title: Re: Inheritance problem
Post by towr on Sep 3rd, 2007, 6:19am
Meh, I'm not too fond of it myself. Generally I'm all for giving solutions in every possible base; but it's contrived to write amounts of dollar in other bases than decimal. I mean, dollars have cents, you can't have cents in [hide]base 9[/hide].
And it doesn't get better when in some cases it's a non-decimal base, and in other cases (like hints) it is.

If I can pick any base to give the answer, I'd say they each get $10.
For the appropriate base it's always true (If they get X, choose base X).

Don't mind me though; you can't please everyone, and maybe I'll like the next one better than Barukh to even it out ;)
Title: Re: Inheritance problem
Post by Grimbal on Sep 3rd, 2007, 9:02am
It seems these work:
[hide]9, 13, 14, 16, 16, 20, 21, 23, 27, 28, ....[/hide]
Title: Re: Inheritance problem
Post by pex on Sep 3rd, 2007, 9:42am

on 09/03/07 at 02:49:43, Barukh wrote:
Why? I agree only wtih a half of these.

Besides, I think you missed a few.
Yeah, I must have made a typo copying 14148167 to Excel. My results now match Grimbal's: 0, 2, or 6 (mod 7).
Title: Re: Inheritance problem
Post by srn347 on Sep 3rd, 2007, 9:52am
Binary.
Title: Re: Inheritance problem
Post by Barukh on Sep 3rd, 2007, 9:52am

on 09/03/07 at 09:42:46, pex wrote:
Yeah, I must have made a typo copying 14148167 to Excel. My results now match Grimbal's: 0, 2, or 6 (mod 7).

By the way, witout even converting from a specific base, it is immediate that the last group (i.e. 6 mod 7) will work.

How?  ;)
Title: Re: Inheritance problem
Post by srn347 on Sep 3rd, 2007, 11:52am
6 mod 7? What is that supposed to mean?!
Title: Re: Inheritance problem
Post by pex on Sep 3rd, 2007, 12:05pm

on 09/03/07 at 11:52:59, srn347 wrote:
6 mod 7? What is that supposed to mean?!

A number is equivalent to 6 (mod 7) if its remainder, when dividing by 7, is equal to 6. Thus, 6, 13, 20, 27, ... are all equivalent to 6 (mod 7).
Title: Re: Inheritance problem
Post by mikedagr8 on Sep 3rd, 2007, 2:25pm
Thanks for the feedback. I did say the puzzle was a little dodgy. It's not mine, it's what I was told in my maths class. Hopefully I can find a puzzle in which everyone is hard working it out and there are no compliants with being a dodgy answer  :).
Title: Re: Inheritance problem
Post by srn347 on Sep 3rd, 2007, 8:27pm
Interesting.
Title: Re: Inheritance problem
Post by mikedagr8 on Sep 8th, 2007, 3:26am

on 09/03/07 at 09:52:58, Barukh wrote:
By the way, witout even converting from a specific base, it is immediate that the last group (i.e. 6 mod 7) will work.

How?  ;)


Because with one more dollar, it will divide by seven evenly.
Title: Re: Inheritance problem
Post by Barukh on Sep 8th, 2007, 4:08am

on 09/08/07 at 03:26:35, mikedagr8 wrote:
Because with one more dollar, it will divide by seven evenly.

Didn't get that. Please elaborate.
Title: Re: Inheritance problem
Post by mikedagr8 on Sep 8th, 2007, 4:17am
If the total was 14148168 instead of 14148167, it would have divided with no remainder. And because we have 6 remainder when dividing by 7, we would have no remainder when dividing 14148168.
Title: Re: Inheritance problem
Post by Barukh on Sep 8th, 2007, 11:36am

on 09/08/07 at 04:17:45, mikedagr8 wrote:
If the total was 14148168 instead of 14148167, it would have divided with no remainder.

Divided by what? And how do you know that without converting from appropriate base?
Title: Re: Inheritance problem
Post by mikedagr8 on Sep 8th, 2007, 5:27pm

on 09/08/07 at 11:36:19, Barukh wrote:
Divided by what? And how do you know that without converting from appropriate base?


I told the puzzle, leave me alone now.  :-X
I haven't been taught mod(s), so I was just having a go because your question was unanswered. Would you like to tell me how it is so obvious?
Title: Re: Inheritance problem
Post by Barukh on Sep 8th, 2007, 11:30pm

on 09/08/07 at 17:27:03, mikedagr8 wrote:
I told the puzzle, leave me alone now.  :-X

No comments.


Quote:
I haven't been taught mod(s)

Have you been taught divisibility rules (http://en.wikipedia.org/wiki/Divisibility_rule)?

I will give you a hint: consider even and odd digits of the total $ separately.
Title: Re: Inheritance problem
Post by mikedagr8 on Sep 9th, 2007, 3:19am

on 09/08/07 at 23:30:43, Barukh wrote:
No comments.

Have you been taught divisibility rules (http://en.wikipedia.org/wiki/Divisibility_rule)?

I will give you a hint: consider even and odd digits of the total $ separately.



Quote:
Second Method Example
Another, more complicated, method uses the fact that 100 ≡ 1, 101 ≡ 3, 10² ≡ 2, 10³ ≡ 6, 104 ≡ 4, 105 ≡ 5, 106 ≡ 1, ... (mod 7). Take each digit of the number (371) in reverse order (173), multiplying them successively by the digits 1, 3, 2, 6, 4, 5, repeating with this sequence of multipliers as long as necessary (1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, ...), and adding the products (1x1 + 7x3 + 3x2 = 1 + 21 + 6 = 28). The original number is divisible by 7 if and only if the number obtained using this procedure is divisible by 7 (hence 371 is divisible by 7 since 28 is).


Applied to 14148167 is 76184141. Now applying the rule: (7*1 + (6*3) + (1*2) + (8*6) + (4*5) + (1*1) + (4*3) + (1*2) =

             7 + 18 + 2 + 48 + 20 + 1 + 12 + 2 = 110 which is not divisible by 7. So from here how would I show that it is 6 (mod 7)? Because the remainder still doesn't work out, becuase the remainder is 5 not 6. Is it because the next number to be used is a 6, hence it will mean that anything in that group is divisible?

[edit] Thanks TR, I was eating desert, and had a typo originally, then added the mistake. [/edit]
Title: Re: Inheritance problem
Post by TenaliRaman on Sep 9th, 2007, 3:30am

on 09/09/07 at 03:19:10, mikedagr8 wrote:
Applied to 14148167 is 76184141. Now applying the rule: (7*1 + (6*3) + (1*2) + (8*6) + (4*5) + (1*1) + (4*3) + (1*2) =   7 + 18 + 2 + 18 + 20 + 1 + 12 + 2 = 70

The sum comes to 110 and not 70.

-- AI
Title: Re: Inheritance problem
Post by Barukh on Sep 9th, 2007, 6:05am
Here's the explanation:

Take any number which is 6 mod 7 (for instance, 13). It will be our base. So, we need to prove that 14148167 in base 13 is divisible by 7.

Take 132. What will be its reminder modulo 7? That’s easy: 1. Then, 133 will have the reminder 6, 134 again 1, etc… So, odd powers of 13 will have remainder 6 mod 7, while even powers will have remainder 1 mod 7. But 6 = -1 mod 7. Therefore, if the sum of digits at even places equals to sum of digits at odd places, the number in base 13 will be divisible by 7!

For our particular example: 7 + 1 + 4 + 4 = 16 = 6 + 8 + 1 + 1.

Of course, the same argument works for any other base which is 6 mod 7.

In base 10, which the above link discusses, the corresponding rule will be for divisibility by 11.
Title: Re: Inheritance problem
Post by mikedagr8 on Sep 9th, 2007, 6:17am
Much clearer now thanks a lot.  :D
Title: Re: Inheritance problem
Post by TenaliRaman on Sep 9th, 2007, 7:37am

on 09/09/07 at 06:05:10, Barukh wrote:
Here's the explanation:

Take any number which is 6 mod 7 (for instance, 13). It will be our base. So, we need to prove that 14148167 in base 13 is divisible by 7.
<snip><snip>
In base 10, which the above link discusses, the corresponding rule will be for divisibility by 11

Interestingly,
(7)10 is (11)6.

Is it just a coincidence? I dont know, i haven't tested this yet. Just thought of it as i reading your post.

-- AI


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