Thursday, 5 November 2015

A Good Party Game: The Magical New Year 2016

This post is a departure from my usual ramblings.
My daughter pointed it out to me and my 10 year old granddaughter was fascinated by the magic of nine.
I thought that it might be worthwhile putting it out here as an interesting extension of the post circulating on social media.

Essentially, the New Year 2016 shows the following 'magical' property:

Add all the digits in 2016:        they add up to number 9
Divide 2016 by 2:  1008:  the digits add up to number 9
Divide 1008 by 2:    504:  the digits add up to number 9
Divide  504  by 2:    252;  the digits add up to number 9
Divide  252  by 2:    126:  the digits add up to number 9
Divide  126  by 2:      63:  the digits add up to number 9
Divide   63  by 2:      31.5 :  the digits add up to number 9
Divide   31.5  by 2:   15.75 :  the digits add up to number 18 which then add up to 9
Divide   15.75  by 2:   7.875 :  the digits add up to number 27 which then add up to 9
.
.
You can continue the division by 2 for ever but the sum of digits in the answer will always be number 9
Is that not magical?

(If you are using a calculator, then watch that after a certain number of division, the display will not show all the digits and the sum may not add up as expected.)

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The answer to the conundrum is very simple.
Essentially, any number that is divisible by 9 will have the sum of its digits add up to 9.
2016 is divisible by 9
If we divide 2016 by 2 any number of times, the number remaining will still have 9 as one of its factors and hence the sum of its digits will still add up to 9.

This is also true for the angle in a circle that is 360 degrees.  You can divide 360 by 2, 5 or 10 any number of times and the resulting angle will still have its digits add to 9.

It is really that simple but can be very perplexing for people in a party atmosphere!

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