Math Is Fun Forum

khushro

Member

Registered: 2015-04-10

Posts: 2

Starter puzzle on this site "12 Days Of Christmas"

The solution was very disappointing. It was just a straight-forward counting of the number of objects, which even an idiot with a calculator can do. There was nothing puzzling about it.
I was expecting a more mathematical solution, which would give the correct answer for n days instead of 12, and then substitute n=12 in the answer. Would not remain a starter, but would at least be a puzzle.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,877

Re: Starter puzzle on this site "12 Days Of Christmas"

Hi khushro,

Yes, the given solution method is rather starter-ish.

A more satisfying solution exists, however, which by way of a nice mathematical formula in terms of n eliminates all that counting and will instantly display the answer for n (eg, n=12) days.

The formula can be found on the net, but, if you'd like to have a go at constructing it yourself, then here are a couple of hints (should you need them):

Last edited by phrontister (2015-05-20 13:58:17)

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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

Laatokka

Member

Registered: 2016-06-07

Posts: 1

Re: Starter puzzle on this site "12 Days Of Christmas"

Hi,

And if you want, you can try making a little program and modify it

(JavaScript)
var x = 1;
var y = 2;
var days = 1;
var PresentsPerDay = 0;

while (days < 13){
  PresentsPerDay=x+PresentsPerDay;
  x=x+y;
  y++;
  days++;

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,877

Re: Starter puzzle on this site "12 Days Of Christmas"

True!

A similar program in BASIC:

    x=1
    y=2
    d=1
    ppd=0
    WHILE d<13
        ppd=ppd+x
        x=x+y
        y=y+1
        d=d+1
    WEND
    PRINT ppd

And...welcome to the forum!

Last edited by phrontister (2016-06-07 23:10:17)

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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

chinnu03

Member

Registered: 2018-08-08

Posts: 1

Re: Starter puzzle on this site "12 Days Of Christmas"

I have found the general solution for this puzzle,

For number of days = n
Total Presents = n(n+1)(n+2)/6

This can be derived as follows
Presents for n'th day = n(n+1)/2 because it is the sum of numbers from 1 to n.
Total presents till n'th day = Σ n(n+1)/2
Simplifying we will get the above formula

Hope it is helpful.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Starter puzzle on this site "12 Days Of Christmas"

hi chinnu03

Welcome to the forum.

Good result.  But I'm afraid it has been done before.  This was, for a while, a GCSE maths project in the UK.  You'd get a grade 'C' for what you have posted but would need to show the whole proof and try possible extensions to get an 'A'.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob