Find the odd ball out

8ball.md

8 ball problem

Of 8 balls one of them is a different weight. The only way to find the different ball is to use a scale. Find the odd ball (no pun intended) and determine if it's heavier or lighter than the rest.

Solution summary

Use a decision tree to deduce what balls need to be removed.

Max number of weighings: 3 #####Notes:

• Finding normal balls for reference in the 2 ball series is trivial so I won't reference finding them.
• Numbers in an array represent balls on one side of a scale like "[1, 2, 3]".

6 ball series

Start by weighing 6 balls - three on each side

6.1

  [1, 2, 3] > [4, 5, 6]
    run 4 ball series with [1, 2, 3, 4]

6.2

  [1, 2, 3] < [4, 5, 6]
    run 4 ball series with [1, 2, 3, 4]

6.3

  [1, 2, 3] = [4, 5, 6]
    run 2 ball series with [7, 8]

4 ball series

4.1

  [1, 2] > [3,4]

  swap ball 2 & 3

  [1, 3] > [2, 4]
    run 2 series with [1, 4]
    if 1.3 -> 4 is light
    if 1.1 -> 1 is heavy
    * 1 cannot be light
    * 4 cannot be heavy

4.2

  [1, 2] = [3,4]
  run 2 series with [5, 6]

4.3

  [1, 2] < [3,4]

  swap ball 2 & 3
    if 1.3 -> 2 is heavy
    if 1.2 -> 1 is light
    * 1 cannot be heavy
    * 4 cannot be light

2 ball series

Listing 2 ball outcomes here for easyier reference. 'n' denotes a normal ball.

1.1

  1 > n

1.2

  1 < n

1.3

  1 = n