# A Really Sweet (and Hard) Math Problem **URL:** \ **Category:** Fun & Games\ **Created:** [February 8, 2007, 2:21pm UTC](https://tw.forumosa.com/t/a-really-sweet-and-hard-math-problem/35632 "2007-02-08T14:21:43Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![miltownkid](https://forumosa-12829.kxcdn.com/user_avatar/tw.forumosa.com/miltownkid/32/46891_2.png) [@miltownkid](https://tw.forumosa.com/u/miltownkid)\ **Post date:** [February 8, 2007, 2:21pm UTC](https://tw.forumosa.com/t/a-really-sweet-and-hard-math-problem/35632/1 "2007-02-08T14:21:43Z")
Wife came home and told me this one. It’s not easy (though it looks it at first.) You have 12 bricks and one of those justice style scales: ![](http://www.lawandjustice.org.uk/scale.gif) They all look the same, except one brick’s weight is different (maybe heavy, maybe light.) Figure out the odd brick in 3 weighing attempts. ---
**Author:** ![Jaboney](https://forumosa-12829.kxcdn.com/user_avatar/tw.forumosa.com/jaboney/32/46120_2.png) [@Jaboney](https://tw.forumosa.com/u/Jaboney)\ **Post date:** [February 8, 2007, 2:36pm UTC](https://tw.forumosa.com/t/a-really-sweet-and-hard-math-problem/35632/2 "2007-02-08T14:36:20Z")
I got it. Answer below so as not to spoil it. > [@](#): > > Weigh all 12, six on each side. The side that rises has the light brick. > Weigh those six, three to a side. The side that rises has the light brick. > Pick two of those three, weigh them one to a side. If one rises, it’s light. If balanced, it’s the third brick. ---
**Author:** ![ImaniOU](https://forumosa-12829.kxcdn.com/letter_avatar_proxy/v4/letter/i/a587f6/32.png) [@ImaniOU](https://tw.forumosa.com/u/ImaniOU)\ **Post date:** [February 8, 2007, 2:41pm UTC](https://tw.forumosa.com/t/a-really-sweet-and-hard-math-problem/35632/3 "2007-02-08T14:41:28Z")
Four against four. If one is heavier, then two against two and then one against one. If they are the same, then weigh the other four as a two against two and… damn, it could be heavier or lighter. Nevermind. ---
**Author:** ![miltownkid](https://forumosa-12829.kxcdn.com/user_avatar/tw.forumosa.com/miltownkid/32/46891_2.png) [@miltownkid](https://tw.forumosa.com/u/miltownkid)\ **Post date:** [February 8, 2007, 2:41pm UTC](https://tw.forumosa.com/t/a-really-sweet-and-hard-math-problem/35632/4 "2007-02-08T14:41:29Z")
> [@Jaboney](#): > > I got it You sure? I said that like 5 times. 😉 Edit: You have to figure out multiple paths if you know what I mean. You’ll solve it one way, and then you’ll notice that it won’t work another. ---
**Author:** ![miltownkid](https://forumosa-12829.kxcdn.com/user_avatar/tw.forumosa.com/miltownkid/32/46891_2.png) [@miltownkid](https://tw.forumosa.com/u/miltownkid)\ **Post date:** [February 8, 2007, 2:43pm UTC](https://tw.forumosa.com/t/a-really-sweet-and-hard-math-problem/35632/5 "2007-02-08T14:43:54Z")
[quote=“Jaboney”]I got it. Answer below so as not to spoil it.[/quote] It might be light OR heavy, that is unknown. ---
**Author:** ![Jaboney](https://forumosa-12829.kxcdn.com/user_avatar/tw.forumosa.com/jaboney/32/46120_2.png) [@Jaboney](https://tw.forumosa.com/u/Jaboney)\ **Post date:** [February 8, 2007, 2:45pm UTC](https://tw.forumosa.com/t/a-really-sweet-and-hard-math-problem/35632/6 "2007-02-08T14:45:36Z")
Ok. Assuming it’s light. Don’t matter, I broke that bad boy. Where’s my Crackerjack prize? ---
**Author:** ![miltownkid](https://forumosa-12829.kxcdn.com/user_avatar/tw.forumosa.com/miltownkid/32/46891_2.png) [@miltownkid](https://tw.forumosa.com/u/miltownkid)\ **Post date:** [February 8, 2007, 2:48pm UTC](https://tw.forumosa.com/t/a-really-sweet-and-hard-math-problem/35632/7 "2007-02-08T14:48:17Z")
[quote=“Jaboney”]Ok. Assuming it’s light. Don’t matter, I broke that bad boy. Where’s my Crackerjack prize?[/quote] You can’t assume it’s light. That makes it a lot easier. In your solution. [quote]Weigh all 12, six on each side. The side that rises has the light brick. Weigh those six, three to a side. The side that rises has the light brick. Pick two of those three, weigh them one to a side. If one rises, it’s light. If balanced, it’s the third brick.[/quote] This wouldn’t work because when you get to your last step, if it’s not balanced, you don’t know which one it is. Note: Actually, the very first step is flawed. ---
**Author:** ![Jaboney](https://forumosa-12829.kxcdn.com/user_avatar/tw.forumosa.com/jaboney/32/46120_2.png) [@Jaboney](https://tw.forumosa.com/u/Jaboney)\ **Post date:** [February 8, 2007, 2:55pm UTC](https://tw.forumosa.com/t/a-really-sweet-and-hard-math-problem/35632/8 "2007-02-08T14:55:09Z")
What are you talking about??? Ok, I see. I assume we knew if it was heavy or light. hmmm… ---
**Author:** ![miltownkid](https://forumosa-12829.kxcdn.com/user_avatar/tw.forumosa.com/miltownkid/32/46891_2.png) [@miltownkid](https://tw.forumosa.com/u/miltownkid)\ **Post date:** [February 8, 2007, 3:01pm UTC](https://tw.forumosa.com/t/a-really-sweet-and-hard-math-problem/35632/9 "2007-02-08T15:01:41Z")
> [@Jaboney](#): > > What are you talking about??? Ok, I see. I assume we knew if it was heavy or light. hmmm… I did the same thing. 😛 ---
**Author:** ![Stray\_Dog](https://forumosa-12829.kxcdn.com/letter_avatar_proxy/v4/letter/s/a587f6/32.png) [@Stray\_Dog](https://tw.forumosa.com/u/Stray_Dog)\ **Post date:** [February 8, 2007, 3:02pm UTC](https://tw.forumosa.com/t/a-really-sweet-and-hard-math-problem/35632/10 "2007-02-08T15:02:40Z")
Weigh four on each side. (1a) If balanced, weigh two of the remaining four. (1b) If balanced, it must be one of the two remaining. Take one and put it on one side and one of the first ones weighed and put it on the other side. The original brick is standard weight, so the scales will show you if the other brick is light or heavy. (1b) If not balanced, weigh one against an original brick. You know which side was heavier before, so you now know if the brick remaining is light or heavy (if the scales tip), or if the one removed is light or heavy (because the scales will now be balanced). OK, I’m working on the other scenario now … ---
**Author:** ![miltownkid](https://forumosa-12829.kxcdn.com/user_avatar/tw.forumosa.com/miltownkid/32/46891_2.png) [@miltownkid](https://tw.forumosa.com/u/miltownkid)\ **Post date:** [February 8, 2007, 3:09pm UTC](https://tw.forumosa.com/t/a-really-sweet-and-hard-math-problem/35632/11 "2007-02-08T15:09:10Z")
> [@Stray Dog](#): > > OK, I’m working on the other scenario now … If you get it, be careful not to spoil it for the others. The force is strong in this one. You’re missing a key point that putting your thoughts on paper might reveal. ---
**Author:** ![Stray\_Dog](https://forumosa-12829.kxcdn.com/letter_avatar_proxy/v4/letter/s/a587f6/32.png) [@Stray\_Dog](https://tw.forumosa.com/u/Stray_Dog)\ **Post date:** [February 8, 2007, 3:18pm UTC](https://tw.forumosa.com/t/a-really-sweet-and-hard-math-problem/35632/12 "2007-02-08T15:18:14Z")
Oh, wait! I don’t have to find the brick and whether it’s light or heavy - just find the odd brick, right? ---
**Author:** ![miltownkid](https://forumosa-12829.kxcdn.com/user_avatar/tw.forumosa.com/miltownkid/32/46891_2.png) [@miltownkid](https://tw.forumosa.com/u/miltownkid)\ **Post date:** [February 8, 2007, 3:20pm UTC](https://tw.forumosa.com/t/a-really-sweet-and-hard-math-problem/35632/13 "2007-02-08T15:20:48Z")
> [@Stray Dog](#): > > Oh, wait! I don’t have to find the brick and whether it’s light or heavy - just find the odd brick, right? That’s right. I’ll give another hint. There basically ends up being 3 paths to success. Two of these paths tells you which brick and the weight. One path just tells you which bring. Is there a proper note taking method for figuring out problems like this? Mine ended up as a bunch of scribbles with scales and pictures. ---
**Author:** ![miltownkid](https://forumosa-12829.kxcdn.com/user_avatar/tw.forumosa.com/miltownkid/32/46891_2.png) [@miltownkid](https://tw.forumosa.com/u/miltownkid)\ **Post date:** [February 8, 2007, 4:29pm UTC](https://tw.forumosa.com/t/a-really-sweet-and-hard-math-problem/35632/14 "2007-02-08T16:29:03Z")
> [@miltownkid](#): > > [quote=“Stray Dog”]Oh, wait! I don’t have to find the brick and whether it’s light or heavy - just find the odd brick, right? That’s right. I’ll give another hint. There basically ends up being 3 paths to success. Two of these paths tells you which brick and the weight. One path just tells you which bring.[/quote] I take that back. You will always find out whether it is heavier or lighter. ---
**Author:** ![twocs](https://forumosa-12829.kxcdn.com/letter_avatar_proxy/v4/letter/t/82dd89/32.png) [@twocs](https://tw.forumosa.com/u/twocs)\ **Post date:** [February 8, 2007, 4:51pm UTC](https://tw.forumosa.com/t/a-really-sweet-and-hard-math-problem/35632/15 "2007-02-08T16:51:28Z")
There are only a few ways to evenly divide the bricks for the first balancing: {6,6}, {4,4,4}, {3, 3, 3, 3}, or {2, 2, 2, 2, 2, 2}. Since nobody has so far had much luck with the groups of 4s, maybe another of these groups could be a possibility. ---
**Author:** ![Edgar\_Allen](https://forumosa-12829.kxcdn.com/letter_avatar_proxy/v4/letter/e/848f3c/32.png) [@Edgar\_Allen](https://tw.forumosa.com/u/Edgar_Allen)\ **Post date:** [February 8, 2007, 6:27pm UTC](https://tw.forumosa.com/t/a-really-sweet-and-hard-math-problem/35632/16 "2007-02-08T18:27:30Z")
I think I have seen this before but the best I can do tonight with certainty is 4 weighs. If you knew whether it was either light of heavy then 3 is straight forward. You have to group in 4’s initially to minimise the chances. Are the rules definitely that there are only 3 weighs, or is it that you can only weigh each brick 3 times? ---
**Author:** ![miltownkid](https://forumosa-12829.kxcdn.com/user_avatar/tw.forumosa.com/miltownkid/32/46891_2.png) [@miltownkid](https://tw.forumosa.com/u/miltownkid)\ **Post date:** [February 9, 2007, 12:02am UTC](https://tw.forumosa.com/t/a-really-sweet-and-hard-math-problem/35632/17 "2007-02-09T00:02:26Z")
> [@Edgar Allen](#): > > Are the rules definitely that there are only 3 weighs, or is it that you can only weigh each brick 3 times? Just 3 attempts. ---
**Author:** ![SuperS54](https://forumosa-12829.kxcdn.com/user_avatar/tw.forumosa.com/supers54/32/137985_2.png) [@SuperS54](https://tw.forumosa.com/u/SuperS54)\ **Post date:** [February 9, 2007, 12:06am UTC](https://tw.forumosa.com/t/a-really-sweet-and-hard-math-problem/35632/18 "2007-02-09T00:06:17Z")
It’s the small blue brick and it’s lighter than those big red ones. ---
**Author:** ![cfimages](https://forumosa-12829.kxcdn.com/user_avatar/tw.forumosa.com/cfimages/32/175176_2.png) [@cfimages](https://tw.forumosa.com/u/cfimages)\ **Post date:** [February 9, 2007, 12:53am UTC](https://tw.forumosa.com/t/a-really-sweet-and-hard-math-problem/35632/19 "2007-02-09T00:53:30Z")
Is it only a little bit heavier/lighter, or a lot? Or don’t we know? Coz if it’s a lot heavier/lighter, you could take an educated guess by feel before you weighed. Or - post the question on a web forum asking for other peoples solutions. Then, when they have a solution, use this as your answer. That way, you wouldn’t need 3 weighing attempts. ---
**Author:** ![miltownkid](https://forumosa-12829.kxcdn.com/user_avatar/tw.forumosa.com/miltownkid/32/46891_2.png) [@miltownkid](https://tw.forumosa.com/u/miltownkid)\ **Post date:** [February 9, 2007, 3:37am UTC](https://tw.forumosa.com/t/a-really-sweet-and-hard-math-problem/35632/20 "2007-02-09T03:37:54Z")
> [@cfimages](#): > > Is it only a little bit heavier/lighter, or a lot? Or don’t we know? because if it’s a lot heavier/lighter, you could take an educated guess by feel before you weighed. Oh, I forgot to mention that the bricks are encased in a glass box and you have to use robotic arms to move them around thus nullifying the ability to judge weight based on feel. > [@cfimages](#): > > Or - post the question on a web forum asking for other peoples solutions. Then, when they have a solution, use this as your answer. That way, you wouldn’t need 3 weighing attempts. Well, you would need the correct solution for each new scenario, so it’s necessary to understand how the three steps work. > [@SuperS54](#): > > It’s the small blue brick and it’s lighter than those big red ones. Close but no toe cheese. [Next page](https://tw.forumosa.com/t/a-really-sweet-and-hard-math-problem/35632.md?page=2)