30th September 2023, 11:30 am
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—What’s the best way to get a math tutor?
—An add!
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—Why was the equal sign so humble?
—Because she knew she wasn’t greater than or less than anyone else.
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—Where do mathematicians go on vacation?
—Times Square.
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—Why do cheapskates make good math teachers?
—Because they make every penny count.
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—Why was math class so long?
—The teacher kept going off on a tangent.
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—What did the student say about the calculus equation she couldn’t solve?
—This is derive-ing me crazy!
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—Did you hear about the statistician who drowned crossing a river?
—It was three feet deep, on average.
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—What do organic mathematicians throw into their fireplaces?
—Natural logs.
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—Why is the obtuse triangle always upset?
—It is never right.
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—What is the integral of one divided by a cabin? A log cabin?
—No, houseboat — you forgot the C.
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16th September 2023, 02:53 pm
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—What do you get when a bunch of sheep hang out in a circle?
—Shepherd’s pi.
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—What do you call a metric cookie?
—A gram cracker.
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—What state has the most math teachers?
—Math-achusetts.
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—What does a hungry math teacher like to eat?
—A square meal.
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—What is the mathematician’s favorite season?
—Sum-mer.
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—What adds, subtracts, multiplies, divides, and bumps into light bulbs?
—A moth-ematician.
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—What tools do you use for math?
—Multi-pliers.
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—Why didn’t the quarter roll down the hill with the nickel?
—Because it had more cents!
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—Which snakes are good at math?
—Adders.
* * *
—What is the butterfly’s favorite subject in school?
—Moth-ematics.
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13th September 2023, 12:29 pm
The Ural Math Battle in 2016 had several mafia-themed problems of various difficulty with the same initial setup.
Puzzle Setup. Among 100 residents of Saint-San, m are mafiosi, and the rest are civilians. A commissioner arrived to the town after getting this information. In an attempt to expose the mafia, this commissioner asked each of the residents to name s mafia suspects from among the other 99 residents. The commissioner knows that none of the mafiosi would name other mafiosi, but each civilian would name at least k mafia members. What is the maximum number of mafia members the commissioner can definitively identify after his survey?
- The most difficult case was m = s = 3 and k = 2.
- In the next case, where m = 3 and s = k = 2, the puzzle had a different task: prove that the commissioner can find at least one mafioso.
- In the third case, where m = s = 10 and k = 6, the question was whether the commissioner can find at least three mafiosi.
- In the fourth case, where m = s = 10 and k = 7, the question was whether the commissioner can find all the mafiosi.
- The last case was for younger students with m = 6, s = 10, and k = 6. The question was whether the commissioner can find all the mafiosi.
When I asked ChatGPT to translate the first and the most difficult case of this puzzle from Russian, ChatGPT decided to solve it too. At the end of its ridiculous solution, it concluded that the commissioner could identify all 21 mafiosi out of the given 3. So, if you comment on this blog that the answer to the first case is 21, I will know that you are a bot.
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3rd September 2023, 04:57 pm
I recently saw another puzzle on Facebook, a generalization of a problem from the 2002 Belarus Olympiad. In the problem, there are red and white boxes. Given how Russia and Belarus are filled with propaganda, my first question was whether the Belarusian flag was red and white. But in fact, the official flag is red and green; however, the opposition uses a red and white one. It could either be a coincidence or a sneaky way of protesting. Anyway, here is the problem.
Puzzle. There are two boxes filled with candy. The red box has R candies, and the white box has W candies. Alice and Bob are playing a game where Alice starts, and both players have the same options each turn: Either move one candy from the red box to the white box or take two candies from any box and eat them. The player who can’t move loses. For which values of R and W is each of the following true?
- Alice, following her optimal strategy, wins but might lose if she makes a mistake.
- Alice wins no matter what.
- Bob, following his optimal strategy, wins but might lose if he makes a mistake.
- Bob wins no matter what.
The list of options is weird, but I decided to keep it to emphasize …. Oops, I do not want to spoil it. You can decide for yourself what I wanted to emphasize.
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