Math Is Fun Forum

Yusuf

Guest

maths puzzle

I was given the following puzzle to solve:-

Using 1,3,5,7,9,11,13 and 15, ADD 3 numbers together to reach a total of 30. (you can use a number more than once).

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: maths puzzle

Hi;

You have been given an impossible task. There are no solutions.

(2 n + 1) + (2 m + 1) + (2 p + 1) = 3 + 2 m + 2 n + 2 p

The terms on the LHS represent 3 odd numbers. The expression on the right which is clearly odd represents their sum. 30, is not an odd number so it can not be represented. Also, it should be clear that even if any of the numbers are duplicates there will always be a constat of 3 on the rhs.

A bit of fun uses a generating function to prove the above:

You will notice that the x^30 term is missing.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,895

Re: maths puzzle

Hi Yusuf;

The sum of three odd numbers will always result in an odd number, and as all the numbers in the list are odd and the answer is even, there is no solution.

Edit: Oops - wasn't watching. bobbym beat me to it.

Last edited by phrontister (2015-04-07 20:38:15)

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"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

math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

Re: maths puzzle

Hey there, y'all. Both bobbym and phrontister are right. It is pretty obvious that the task is certainly impossible.
[Even if we brought back Einstein, Newton, Pythagoras or any of those folks from the dead, they certainly could not solve it. - LOL ;-) ]

3 odd numbers can NEVER sum an even number.
Who created this puzzle anyway? (Oops, hope that ain't offensive!) Did he/she know beforehand that it's got no solution and is perhaps only trying to pull someone's legs?

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Only a friend tells you your face is dirty.

math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

Re: maths puzzle

I appreciate folks like bobbym, and phrontister of course, who are eager to help out. Indeed we really got some mathematicians (or mathematicians in the making) on the forum.

Thumbs up, guys!

Hmm, when will I reach that level too.

And, oh! Lest i forget, thanks guest for sharing info.

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Only a friend tells you your face is dirty.