Brain teaser: 12 cricket balls

This one’s an old one, but a good one. Some of you may have seen it before. 

You are given twelve cricket balls. 

(For readers on the other side of the Pond, cricket is the finest of all sports, and you really don’t know what you’re missing. But let us not digress.) 

You are given 12 cricket balls, which look identical, but one of them is a bit different from the other eleven. Although it looks like the other eleven, it doesn’t weigh the same. It could be lighter, or it could be heavier. You don’t know. 

The other eleven balls all weigh the same as each other. 

And you also have one of those old-fashioned scales. You can put as many balls as you like on either side of the scales, and you will know whether the two sides are equal in weight, or whether one side is heavier than the other. And that is all.

You are allowed to use these scales three times, and three times only. And from that, you must identify the ball that doesn’t weigh the same as the others. And you must be able to say whether it is heavier or lighter than the others.

Over to you. (Answer some time next week.)

(Hint: don’t start with weighing 6 balls on one side against 6 on the other: all that will tell you is that either one of the balls on the lighter side is light, or that one of the balls on the heavier side is heavy. And that doesn’t really get you too far.)

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7 responses to this post.

  1. Posted by Erika W. on June 23, 2011 at 5:44 pm

    Haven’t had any coffee yet today! However this reminds me of a brain teaser which I w sh I could remember: A group of men come to an inn and there are not enough beds. By various twists it ends up seeming that there are enough beds after all–it is dependent upon unintentionally miscounting your fingers a few times. Do you know this one?

    Reply

    • I think I heard somethinvg like that one – say you have 4 beds and 5 people, then, temporarily, you put two people into the first bed, then put Person 3 into Bed 2, Person 4 into Bed 3, and of the 2 people you had initially put into one bed, you bring one of them out and put him, Person 5, into Bed 4, thus accommodating everyone. And then you quickly change the subject before anyone has time to figure out you’re being silly! 🙂

      Is that the one?

      Reply

  2. Many people make the mistake of assuming that on each weighing they can only get two bits of infomation ie left pan down or right pan down and 2 to the power of three bits will not solve the problem but of course on each weihging you get three bits left down, balance or right down and three to the power of three are plenty.

    Reply

    • On each weighing, you will get one of three possible outcomes. But of course, you’ll only get one of these three outcomes at any given weighing!

      Good to see you here, by the way!

      Reply

    • Thanks for that, Middle_Aged_Fogey.

      If anyone wants to have a go solving this problem for themselves, may I recommend that you don’t click on Middle_Aged_Fogey’s link right now!

      In any case, the solution on that link refers to pool balls, whereas the problem I present is to do with cricket balls. And that, of course, is a different matter altogether! 🙂

      Reply

  3. Posted by Erika W. on June 30, 2011 at 4:03 pm

    that’s the bed one alright–thank you so much.

    Reply

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