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# Category Archives: challenges

## The broken weight problem

Here’s a fantastic problem I recently heard. Apparently it was first posed by Claude Gaspard Bachet de Méziriac in a book of arithmetic problems published in 1612, and can also be found in Heinrich Dorrie’s 100 Great Problems of Elementary … Continue reading

## The haybaler

At Penn Alexander’s math club yesterday, the students worked on a fun puzzle that I’d never seen before. It goes like this: You have five bales of hay. For some reason, instead of being weighed individually, they were weighed in … Continue reading

## Who Am I?

An excellent puzzle from JD2718: There are five true and five false statements about the secret number. Each pair of statements contains one true and one false statement. Find the trues, find the falses, and find the number. 1a. I … Continue reading

Posted in challenges, logic, number theory, puzzles, teaching
Tagged number, puzzle, secret
13 Comments

## Hyperbinary conjecture seeking proof for a good time, long walks on the beach

Here’s the latest progress on the hyperbinary sequence. We’re trying to figure out the inverse relation of the function : given a particular number , where does it occur in the hyperbinary sequence? That is, what are the values of … Continue reading

Posted in challenges, pattern, people, proof, sequences
Tagged Euler, hyperbinary, inverse relation, totient
4 Comments

## More hyperbinary fun

When I originally posed Challenge #12, a certain Dave posted a series of comments with some explorations and partial solutions to part II (the hyperbinary sequence). Although I gave the “solution” in my last post, no solution to any problem … Continue reading

Posted in challenges, induction, pattern, proof, recursion, sequences, solutions
Tagged hyperbinary, induction
12 Comments

## Challenge #12 solution, part II

Yes, that’s right, that Challenge #12, posted one year, five months, and a day ago. You see, I have this nasty habit of starting things and not finishing them… well, better late than never! Question two of the aforementioned challenge … Continue reading

Posted in challenges, counting, induction, pattern, sequences, solutions
Tagged binary, hyperbinary
15 Comments

## MMM #33: Super divisible

This week’s Monday Math Madness is up at Wild About Math!. Looks like a fairly accessible problem this week: What’s the prime factorization of the smallest whole number that is divisible by all integers from 1 up to and including … Continue reading

Posted in challenges, links, number theory, primes
Tagged divisible, factorization, smallest