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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Heres a puzzle I just created out of the top of my own head.

I once took part in a survey in which a number of people were asked to give their house numbers. I was one of the first 10 people to be asked. At that point, it was found that if you subtracted 2 from the sum of our house numbers, youd get a number which is divisible by 9, while if you added 9 to the sum of our house numbers, youd get a number which is divisible by 10. Then the rest of the people were asked their house numbers, and at the end of the survey, it was found that the total sum of all the house numbers in the survey was a nice round 100.

My house number is an even number. So, whats my house number?

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**ZHero****Real Member**- Registered: 2008-06-08
- Posts: 1,889

If two or more thoughts intersect, there has to be a point!

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**gurthbruins****Member**- Registered: 2010-05-09
- Posts: 157

My answer

*It's the activity of the intelligence above all that gives charm to existence.*

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**gurthbruins****Member**- Registered: 2010-05-09
- Posts: 157

Unusual puzzle!

*It's the activity of the intelligence above all that gives charm to existence.*

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**ZHero****Real Member**- Registered: 2008-06-08
- Posts: 1,889

gurthbruins wrote:

Unusual puzzle!

No doubt!

And It makes use of an

She's a notorious Number Player!!

If two or more thoughts intersect, there has to be a point!

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Interestingly, you can take a shortcut with this puzzle by "meta-thinking", making the assumption that there is a single correct answer.

"I was telling my friend about a survey I took about house numbers. I told her how many houses were surveyed, and the sum of the surveyed house numbers. She knew that my number was even, and then she managed to figure out what my number was.

What's my house number?"

Why did the vector cross the road?

It wanted to be normal.

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**ZHero****Real Member**- Registered: 2008-06-08
- Posts: 1,889

mathsyperson wrote:

Interestingly, you can take a shortcut with this puzzle by "meta-thinking", making the assumption that there is a single correct answer.

"I was telling my friend about a survey I took about house numbers. I told her how many houses were surveyed, and the sum of the surveyed house numbers. She knew that my number was even, and then she managed to figure out what my number was.

What's my house number?"

After thinking for a long while, i figured it out that why it works!

The point is that "1" can not be split further into natural numbers and that house numbers can't be fractions!

I started with putting an upper limit to the sum (which had to be greater than the lowest possible value) and found that in each case, one of the house numbers can be broken down further and thus nothing can be uniquely determined (the number of even and odd numbers also doesn't remain unique )!

But if more conditions are introduced (such as the product of house numbers being maximum/minimum or less than/greater than certain value) then, possibly, a unique solution can be obtained!?

I loved ur "meta-thinking" thing... Is it similar to "lateral-thinking" or something?

If two or more thoughts intersect, there has to be a point!

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

I don't know if that's the correct term, but it's the one I use.

It's essentially when you think about the fact that a puzzle is a puzzle, rather than its content.

Why did the vector cross the road?

It wanted to be normal.

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Youve all got the correct answer, as well as some good ideas, but I hope you didnt neglect the last bit of problem, namely that the total of all the house numbers was 100. This is significant to the solution. Without it, youd only be making an unwarranted assumption.

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**ZHero****Real Member**- Registered: 2008-06-08
- Posts: 1,889

JaneFairfax wrote:

I hope you didnt neglect the last bit of problem, namely that the total of all the house numbers was 100. This is significant to the solution. Without it, youd only be making an unwarranted assumption.

I considered it!!

I figured this out that

Latter doesn't fit in..

If two or more thoughts intersect, there has to be a point!

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

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**ZHero****Real Member**- Registered: 2008-06-08
- Posts: 1,889

JaneFairfax wrote:

Hey... I hate to get lost into ∞

To tell you the truth, i was just bout to wonder if anymore solutions exist when i got lost into "the real world" and by the time i got back, it was You and Your solution!!

Thanks for telling that coz i guess i've started understanding what those notations mean!!

I'm yet to take a Complete "Abstract Algebra" course and I hope to catch up with most of you guys out there pretty soon (well.. most of you wud have covered the "Extra Mile" by then too ; I can equal by an Extra )!

To add... I'm a SLOW LEARNER and am not even STEADY!

Will I ever be able to Win the RACE??

*Last edited by ZHero (2010-05-16 04:22:40)*

If two or more thoughts intersect, there has to be a point!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,783

Hi Jane;

Sorry, but I thought your problem was little bit more difficult than the partition of 11 into 1,1,1,1,1,1,1,1,1,2.

I am not that familiar with your country. Aren't some English homes numbered by halves and may start as zero.?

This is from Wikipedia.

British houses started being numbered with the Postage Act of 1765[3]. In rural areas many houses remain named but un-numbered. The odd numbers will typically, although not always, be on the left-hand side as seen from the centre of the town or village, with the lowest numbers at the end of the street closest to the town centre. Intermediate properties usually have a number suffixed A, B, C, etc., but there are several that have been given a half number, e.g. the old police station at 20½ Camberwell Church Street. At least one property (built next to no.2 after the street had been numbered) has been numbered zero.

If you cannot falsify the above then:

Here are both of my new solutions:

4 , 1/2 , 1/2 , 1/2 , 1/2 , 1 , 1 , 1 , 1 , 1. You live at #4.

6 , 1/2 , 1/2 , 1/2 , 1/2 , 1/2 , 1/2 , 1/2 , 1/2 , 1. You live at #6

With the condition that a house can numbered 0 there are of course, many more.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,374

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**ZHero****Real Member**- Registered: 2008-06-08
- Posts: 1,889

bobbym wrote:

Hi Jane;

Sorry, but I thought your problem was little bit more difficult than the partition of a 11 into 1,1,1,1,1,1,1,1,1,2.

I am not that familiar with your country. Aren't some English homes numbered by halves and may start as zero.?...

Here is one of my solutions then 4 , 1/2 , 1/2 , 1/2 , 1/2 , 1 , 1 , 1 , 1 , 1. You live at #4.

The puzzle, in any such scenario, will not be solveable!!?

Its a "Hyper-Meta-Lateral-Meta-Meta-Thinking"!!

If two or more thoughts intersect, there has to be a point!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,783

I just solved it. Please read before you write. Otherwise we will be confused.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**ZHero****Real Member**- Registered: 2008-06-08
- Posts: 1,889

Oh... I meant...

The puzzle won't be UNIQUELY Solveable.. which is as good (or equivalently bad) as not being able to solve it (i.e. figuring out the house number)!!

One should certainly not overlook this possibility though...

Its better now...

*Last edited by ZHero (2010-05-16 05:42:29)*

If two or more thoughts intersect, there has to be a point!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,783

Hi;

The bounds that we are dealing with integers is not in the question. You cannot assume that for the answer, just because you desire uniqueness. The post was directed at Jane. She is best able to explain it away or verify it. After all, she lives in England and she has created the question. Neither of us live in England. The Wikipedia article may be in error. I do not want to pollute this thread with an endless, unproductive back and forth of who is right. Let's wait until she replies.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,608

[An argument broke out and I couldn't work out the pros and cons of it so I just deleted it all]

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

*Last edited by JaneFairfax (2010-05-18 20:33:05)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,783

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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