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The 12-ball problem is a fun one and IMO the key revelation is that you do not need to determine whether the ball is lighter or heavier (which isn’t possible an

by koolba 4y ago

The 12-ball problem is a fun one and IMO the key revelation is that you do not need to determine whether the ball is lighter or heavier (which isn’t possible anyway). Just which ball is different than the rest. It’s a great exercise in decision trees as you change your strategy based on total information, not just the most recent step. It’s also fun to scale the problem from 3 balls up to see how the solution evolves.

thaumasiotes 4y ago
>> you're given 12 metal balls and told that one of them is either heavier or lighter than the rest. You're then given a balance/scale and instructed to figure out which ball is different and whether it is heavier or lighter using the balance a maximum of three times > The 12-ball problem is a fun one and IMO the key revelation is that you do not need to determine whether the ball is lighter or heavier (which isn’t possible anyway). Huh?
- vgb2k18 4y ago
  If I'm reading this [0] right, the heavier/lighter factor can be determined within 3 weightings... [0] https://suresolv.com/brain-teaser/find-fake-ball-among-12-identical-balls-3-weighing-hard-puzzle-solution https://suresolv.com/brain-teaser/find-fake-ball-among-12-id...
  - thaumasiotes 4y ago
    Of course it can. There are 24 possible states and you get enough information to uniquely identify one of 27 states. This was already stated in the root comment. I'm confused how the response to "you must identify whether the odd ball is heavier or lighter" can be "the key to this is realizing you don't need to know whether the odd ball is heavier or lighter, which is good because that's impossible anyway".
    - vgb2k18 4y ago
      Sorry, yes I saw your confusion. If you read back to your Huh comment you might forgive me for reading it as that you were unsure of the truth yourself. The one word 'huh?', spoke to me as "which one of these is true?". Whereas a person who was sure of the true answer, I would expect to say "Hey that's incorrect", if they encountered an obviously mistaken quote.
hgsgm 4y ago
Scale down first! Interesting patterns start from 0 and 1.

by koolba 4y ago

thaumasiotes 4y ago

>> you're given 12 metal balls and told that one of them is either heavier or lighter than the rest. You're then given a balance/scale and instructed to figure out which ball is different and whether it is heavier or lighter using the balance a maximum of three times > The 12-ball problem is a fun one and IMO the key revelation is that you do not need to determine whether the ball is lighter or heavier (which isn’t possible anyway). Huh?

vgb2k18 4y ago
If I'm reading this [0] right, the heavier/lighter factor can be determined within 3 weightings... [0] https://suresolv.com/brain-teaser/find-fake-ball-among-12-identical-balls-3-weighing-hard-puzzle-solution https://suresolv.com/brain-teaser/find-fake-ball-among-12-id...
- thaumasiotes 4y ago
  Of course it can. There are 24 possible states and you get enough information to uniquely identify one of 27 states. This was already stated in the root comment. I'm confused how the response to "you must identify whether the odd ball is heavier or lighter" can be "the key to this is realizing you don't need to know whether the odd ball is heavier or lighter, which is good because that's impossible anyway".
  - vgb2k18 4y ago
    Sorry, yes I saw your confusion. If you read back to your Huh comment you might forgive me for reading it as that you were unsure of the truth yourself. The one word 'huh?', spoke to me as "which one of these is true?". Whereas a person who was sure of the true answer, I would expect to say "Hey that's incorrect", if they encountered an obviously mistaken quote.

hgsgm 4y ago

Scale down first! Interesting patterns start from 0 and 1.