Brain Teasers
The Cake Disaster 2
One day, in baking class, 15 students were baking cakes when the fire alarm went off. Everyone exited the building, but when they got back, they found someone had dumped all the sugar into two of the batter-filled bowls. Everyone was puzzled over what to do until Alice had an idea: why not mix the batters together and then separate the contents back in the bowls. Here is what happened in chronological order:
Alice mixed with Flare
June pours some into Emma's
Luke mixed with Callie
June mixed with Gabbi
Flare mixed with Gabbi
Watt mixed with Tina
Flare mixed with Tina
Luke mixed with Flare
Gabbi mixed with Callie
Daniel, Emma, & Alice mixed with each other
Oscar mixed with Quinn
Misty mixed with Callie
Alice, Misty, & Oscar mixed with each other
Tina mixed with Emma
Kaleb mixed with Quinn
June mixed with Daniel
Luke mixed with June
Ryan, Luke, & Watt mixed with each other
Callie, Alice, & Flare mixed with each other
Kaleb pours some into Daniel's
Watt mixed with Ryan
Watt pours some into Kaleb's
Daniel mixed with Luke
Misty mixed with Gabbi
Kaleb mixed with Tina
Emma & Quinn had no sugar; which 2 bowls started with sugar?
Everyone was able to figure it out.
Alice mixed with Flare
June pours some into Emma's
Luke mixed with Callie
June mixed with Gabbi
Flare mixed with Gabbi
Watt mixed with Tina
Flare mixed with Tina
Luke mixed with Flare
Gabbi mixed with Callie
Daniel, Emma, & Alice mixed with each other
Oscar mixed with Quinn
Misty mixed with Callie
Alice, Misty, & Oscar mixed with each other
Tina mixed with Emma
Kaleb mixed with Quinn
June mixed with Daniel
Luke mixed with June
Ryan, Luke, & Watt mixed with each other
Callie, Alice, & Flare mixed with each other
Kaleb pours some into Daniel's
Watt mixed with Ryan
Watt pours some into Kaleb's
Daniel mixed with Luke
Misty mixed with Gabbi
Kaleb mixed with Tina
Emma & Quinn had no sugar; which 2 bowls started with sugar?
Everyone was able to figure it out.
Hint
Everyone was able to figure it out.Answer
Luke & CallieTo start, it can't be Emma or Quinn or anyone who mixed/gave to them. This leaves Flare, Luke, Callie, Gabbi, Watt, Misty, and Ryan.
It can't be Flare because he exchanged with Alice before Alice exchanged with Emma. It can't be Watt because he mixed with Tina before Tina exchanged with Emma. This leaves Luke, Callie, Gabbi, Misty, and Ryan.
It can't be Gabbi because she mixed with Flare before Flare mixed with Tina who mixed with Emma later. This leaves Luke, Callie, Misty, and Ryan.
If only one of Luke & Callie started with sugar it wouldn't be solvable because no interactions happened before them and the outcome would be the same, therefore the solution is either Misty and Ryan or Luke and Callie.
However, it can't be Ryan and Misty because they can't give June sugar!
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Wait, what? I don't follow. It seems that there are multiple solutions: (Luke, Callie), (Luke, Ryan), (Luke, Misty), (Callie, Ryan), or (Callie, Misty). These were ambiguous.
You can deduce that at least one of Luke or Callie must start with sugar. I don't see how you get any further.
Saying that everyone could figure it out and then using that fact to figure it out is circular. How did everyone figure it out? How did they eliminate the solutions other than Luke and Callie?
You can deduce that at least one of Luke or Callie must start with sugar. I don't see how you get any further.
Saying that everyone could figure it out and then using that fact to figure it out is circular. How did everyone figure it out? How did they eliminate the solutions other than Luke and Callie?
Would it help if I said it was possible to solve?
I must be missing it. How is it possible?
I use "the puzzle is solvable" in sudoku/star battle puzzles
I find a case where the answer would end up being 2 options, and then I can eliminate that
I find a case where the answer would end up being 2 options, and then I can eliminate that
Hmmm, I don't know if I agree with that.
What I do know is that I had a great time working this puzzle. It was a lot of fun and quite hard. Getting down to the point where one of Luke or Callie must start with sugar was resolution enough for me.
Sometimes it is nice to have a quick distraction of a teaser: you see, you solve, you move on. Sometimes it is nice to have a project for the day. Thank you for this extended and entertaining brain exercise!
I love these puzzles.
What I do know is that I had a great time working this puzzle. It was a lot of fun and quite hard. Getting down to the point where one of Luke or Callie must start with sugar was resolution enough for me.
Sometimes it is nice to have a quick distraction of a teaser: you see, you solve, you move on. Sometimes it is nice to have a project for the day. Thank you for this extended and entertaining brain exercise!
I love these puzzles.
I agree that the logic is circular.
We can't even rule out the possibility of Misty and Ryan having the sugar originally, because we are told only that Emma and Quinn end up with no sugar. This does NOT mean that June ends up with sugar. We might have been able to assume she does if the bakers could solve the problem, but the bakers cannot know whether it is Luke and Callie together, or separately with one of the other possibilities.
We can't even rule out the possibility of Misty and Ryan having the sugar originally, because we are told only that Emma and Quinn end up with no sugar. This does NOT mean that June ends up with sugar. We might have been able to assume she does if the bakers could solve the problem, but the bakers cannot know whether it is Luke and Callie together, or separately with one of the other possibilities.
On second thought, since the bakers would be able to rule out the possibility of Misty and Ryan having the only sugar originally, based on knowing whether or not June ends up with sugar, we CAN eliminate that combination.
However, the bakers can't rule out Misty or Ryan individually, so we can't either.
However, the bakers can't rule out Misty or Ryan individually, so we can't either.
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