Archive for the ‘Puzzles’ Category.
26th October 2024, 03:24 pm
25th October 2024, 12:16 pm
Here is a new report of interesting homework solutions from my students.
Puzzle. One day, two sisters decided to clean the old shed at the bottom of their garden. When they finished cleaning, one had a dirty face and the other had a clean face. The sister with the clean face went and washed her face, but the girl with the dirty face did not wash. Why should this be so?
The expected answer: The sister with the clean face saw her sister’s dirty face and assumed her own face must be dirty as well, so she washed it. The sister with the dirty face saw her sister’s clean face and assumed her own face must also be clean, so she didn’t feel the need to wash.
Another student suggested a different but quite realistic answer.
The realistic answer: The sisters’ home ran out of water after the clean sister washed her face, preventing the dirty sister from washing her own.
The other student watched too many sitcoms.
The sitcom answer: The sister with the dirty face purposefully kept her face dirty, so she could show her parents that she did all the work, as she was the only one with dirt on her face.
I asked ChatGPT to solve the puzzle, and, unsurprisingly, it came up with the standard answer. I pushed and got the following.
The ChatGPT answer: The sister with the clean face washed up because she was an Instagram influencer and couldn’t risk being seen dirty, even in her own garden. Meanwhile, the sister with the dirty face was a carefree adventurer who believed dirt was “nature’s makeup.” Plus, she figured that if she waited long enough, the dirt would either blow away or blend into a trendy new skincare routine—”Exfoliation by Shed Dust.”
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22nd October 2024, 03:32 pm
28th September 2024, 12:33 pm
I love hat puzzles, and this one, posted on Facebook by Konstantin Knop, is no exception.
Puzzle. The sultan decided to test his three sages once again. This time, he showed them five hats: three red and two green. Each sage was blindfolded and had one hat placed on their head. When the sages removed their blindfolds, they could see the hats on the other sages but not their own. The twist in this puzzle is that one of the sages is color-blind and cannot distinguish red from green. The sages are all friends and are aware of each other’s perception of color. The sages are then asked, in order, if they know the color of their hats. Here’s how the conversation unfolded:
- Alice: I do not know the color of my hat.
- Bob: Me too, I do not know the color of my hat.
- Carol: Me too, I do not know the color of my hat.
- Alice: I still do not know the color of my hat?
The question is: Who is color-blind?
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27th September 2024, 02:59 pm
From time to time, the homework for my PRIMES STEP students includes questions that are not exactly mathematical. Last week, we had the following physics puzzle.
Puzzle. A fisherman needed to move a heavy iron thingy from one river’s shore to another. When he put the thingy in his boat, the boat lowered so much that it wasn’t safe to operate. What should he do?
The expected answer: He should attach the thingy to the bottom of the boat. When the object is inside the boat, the boat needs to displace enough water to account for the entire weight of the boat and the thingy. When the thingy is attached to the bottom of the boat, the thingy experiences its own buoyancy. Thus, the water level rises less because the thingy displaces some water directly, reducing the boat’s need to displace extra water. Thus, the amount of weight the fisherman saves is equal to the amount of water that would fit into the shape of this thingy.
As usual, my students were more inventive. Here are some of their answers.
- The fisherman could cut the iron thingy and transport it piece by piece.
- He can swim across and drag the boat with a rope with the thingy inside.
- He can use a second boat to pull the first boat with the thingy in it.
- It is another river’s shore, so he can just take the iron with him to a different river without going over water.
- If the fisherman has extra boat material, heightening the boat’s walls would keep it from sinking.
Also, some funny answers.
- He could fast for a few days, making him lighter.
- He could tie helium balloons to the boat to keep it afloat even after he gets in.
- Wait until winter and slide the boat on ice.
And my favorite answer reminded me of a movie I recently re-watched.
- You’re gonna need a bigger boat.
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10th September 2024, 05:45 pm
11th July 2024, 04:57 pm
I recently posted a symmetry puzzle from Donald Bell. He just sent me another one.
Puzzle. Start with a 30-60-90 triangle (half of an equilateral triangle). Divide it into two 30-60-90 triangles of different sizes by dropping a perpendicular from the right-angled corner to the opposite side. Put the resulting two pieces together to form a symmetrical shape. There are two solutions.
It took me some time to find the second solution. I love this puzzle.
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