Home » Science » Math » Math puzzle: Find the odd ball out

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 {1,2,3,4,5} > {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 {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}
Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Countdown to Carlsen-Anand 2014

World chess championship, SochiNovember 8th, 2014
%d bloggers like this: