## Math puzzle: Find the odd ball out

A friend on chessbomb.com asked a very interesting puzzle. Here it is and my attempt to solve it:

There are 15 balls, one of them has an odd weight (either light or heavy) and all the rest have equal weight. We know one of the 14 balls with the correct weight (good ball). Using 3 weighings on a beam balance we need to figure the odd ball out. We do not need to know if the odd ball is heavy or light.

My attempt at the solution

Let us suppose that the known good ball is {1}

- If {1,2,3,4,5} = {6,7,8,9,10} then odd ball is {11,12,13,14,15}
- If {1,11} = {12,13} then odd ball is {14,15 }
- If {1} = {14} then odd ball is {15}
- If {1} > {14} then light odd ball is {14}
- If {1} < {14} then heavy odd ball is {14}

- If {1,11} > {12,13} then odd ball is {11} (heavy) or (12,13} (light)
- If {12} = {13} then heavy odd ball is {11}
- If {12} > {13} then light odd ball is {13}
- If {12} < {13} then light odd ball is {12}

- If {1,11} < {12,13} then odd ball is {11} (light) or (12,13} (heavy)
- If {12} = {13} then light odd ball is {11}
- If {12} > {13} then heavy odd ball is {12}
- If {12} < {13} then heavy odd ball is {13}

- If {1,11} = {12,13} then odd ball is {14,15 }
- If {1,2,3,4,5} > {6,7,8,9,10} then odd ball is {2,3,4,5,6,7,8,9,10}
- If {2,3,6} = {4,5,7} then light odd ball is {8,9,10}
- If {8} = {9} then light odd ball is {10}
- If {8} > {9} then light odd ball is {9}
- If {8} < {9} then light odd ball is {8}

- If {2,3,6} > {4,5,7} then {2,3} is heavy odd ball or {7} is light odd ball
- If {2} = {3} then light odd ball is {7}
- If {2} > {3} then heavy odd ball is {2}
- If {2} < {3} then heavy odd ball is {3}

- If {2,3,6} < {4,5,7} then {4,5} is heavy odd ball or {6} is light odd ball
- If {4} = {5} then light odd ball is {6}
- If {4} > {5} then heavy odd ball is {4}
- If {4} < {5} then heavy odd ball is {5}

- If {2,3,6} = {4,5,7} then light odd ball is {8,9,10}
- If {1,2,3,4,5} < {6,7,8,9,10} then ball is {1,2,3,4,5,6,7,8,9,10}
- If {2,3,6} = {4,5,7} then heavy odd ball is {8,9,10}
- If {8} = {9} then heavy odd ball is {10}
- If {8} > {9} then heavy odd ball is {8}
- If {8} < {9} then heavy odd ball is {9}

- If {2,3,6} > {4,5,7} then {4,5} is light odd ball or {6} is heavy odd ball
- If {4} = {5} then heavy odd ball is {6}
- If {4} > {5} then light odd ball is {5}
- If {4} < {5} then light odd ball is {4}

- If {2,3,6} < {4,5,7} then {2,3} is light odd ball or {7} is heavy odd ball
- If {2} = {3} then heavy odd ball is {7}
- If {2} > {3} then light odd ball is {3}
- If {2} < {3} then light odd ball is {2}

- If {2,3,6} = {4,5,7} then heavy odd ball is {8,9,10}

## Quote of the day

*“If you have the facts on your side, pound the facts. If you have the law on your side, pound the law. If you have neither on your side, pound the table.”*

-Author unknown to me.

## tips for interpreting scientific claims

One of the tips is : “Regression to the mean can mislead” 🙂

## My chess personality

I took my chess personality quiz at chesspersonality.com and these are my results.

## 12 Pieces of Classical Christmas Music in Case You’re Sick of Mariah Carey

For what it’s worth, I actually like that Mariah Carey Christmas song. I know I’ll take some heat for that, but whatever, I don’t really care. It’s a well-crafted pop song (if that’s possible), which doesn’t sound dated (it’s nearly 20 years old) like most pop music does after like two weeks.

Side note: Mariah Carey could live off the “All I Want For Christmas is You” royalties alone. It’s impossible to chart worldwide royalty numbers, but it is the best-selling Christmas single of all time (12 million copies) on the best-selling Christmas album of all time (more than 15 million copies), and in Great Britain alone, Carey is projected to rake in close to $750,000 this year for that one song.

But if all you want for Christmas is a little more substance in your Christmas music, then this blog’s for you. Below are 12 pieces of classical…

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## A New King for a New Era in Chess

Garry Kasparov’s article in Time magazine on Carlsen’s ascent to the top.

The guard has been changed at the top of the chess world. Last week in Chennai, India, 22-year-old Norwegian prodigy Magnus Carlsen easily toppled defending world champion Viswanathan Anand of India. The challenger won three games without a loss, plus seven draws, ending the match two games before its scheduled length of 12 games.

Carlsen’s domination renders unnecessary any extensive punditry on the match itself. He has been the world’s top-ranked player for two years already while Anand’s results have tailed off, as those of players on the wrong side of forty tend to do. It is true that Anand made quite a few unforced errors in his losses, but as I said before the match, Anand was fighting not only a stronger player but also the tidal forces of time and history. Carlsen is a force of nature whose time has come and there was little Anand could…

View original post 704 more words