It's that time of year again!
Jun. 29th, 2015 01:17 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
theweaselkingToday I do math nerdery and puzzles.
I was looking for the answer to the old one-off marble puzzle[1] because I knew it HAD a solution and I knew it had a SIMPLE solution but I couldn't remember what it was. In the process, I ran into this fun little puzzle:
PUZZLE #1:
"For any prime number greater than 3 (labelled "p") why is it that p2-1 is ALWAYS evenly divisible by 24?"
eg: 5 is prime. 52-1 is 24. 13 is prime. 132-1 is 168, which is 24x9. 17 is prime. 172-1 is 288, which is 24x12. 4027 is prime. 40272-1 is 16216728, which is 24x675697. For ALL prime numbers over 3, the number, squared, minus 1, will be evenly divisible by 24. Why?
In fact, while I'm here, PUZZLE #2
A vending machine dispenses two kinds of chocolate bar. It has three buttons - "Snickers", "Mars", and "Random". Snickers gets you a Snickers bar, Mars gets you a Mars bar, Random gets you either a Snickers or a Mars, 50/50 chance. At least, that's how it's SUPPOSED to work, but the guy who set it up screwed up the labels so none of the labels on the buttons are right. It costs $1 for a chocolate bar; what's the minimum amount of money required to be able to know, for certain, which button is which?
[1]: You know the one, right? You have 12 marbles, identical except one of them is either lighter or heavier than the others. You don't know which is the odd one out or if the odd one is light or heavy. You have only an old-style balance scale to use so you can measure marbles or groups of marbles against each other but not against anything else. Using only this scale, determine which is the odd one, and if it's light or heavy, in no more than 3 weighings. You know what, now that I've written it out, why not throw this out as a question to the audience, too? PUZZLE #3! It's super-old but has a neat counterintuitive solution.
Comments screened, correct answers will stay screened until I post solutions.
I was looking for the answer to the old one-off marble puzzle[1] because I knew it HAD a solution and I knew it had a SIMPLE solution but I couldn't remember what it was. In the process, I ran into this fun little puzzle:
PUZZLE #1:
"For any prime number greater than 3 (labelled "p") why is it that p2-1 is ALWAYS evenly divisible by 24?"
eg: 5 is prime. 52-1 is 24. 13 is prime. 132-1 is 168, which is 24x9. 17 is prime. 172-1 is 288, which is 24x12. 4027 is prime. 40272-1 is 16216728, which is 24x675697. For ALL prime numbers over 3, the number, squared, minus 1, will be evenly divisible by 24. Why?
In fact, while I'm here, PUZZLE #2
A vending machine dispenses two kinds of chocolate bar. It has three buttons - "Snickers", "Mars", and "Random". Snickers gets you a Snickers bar, Mars gets you a Mars bar, Random gets you either a Snickers or a Mars, 50/50 chance. At least, that's how it's SUPPOSED to work, but the guy who set it up screwed up the labels so none of the labels on the buttons are right. It costs $1 for a chocolate bar; what's the minimum amount of money required to be able to know, for certain, which button is which?
[1]: You know the one, right? You have 12 marbles, identical except one of them is either lighter or heavier than the others. You don't know which is the odd one out or if the odd one is light or heavy. You have only an old-style balance scale to use so you can measure marbles or groups of marbles against each other but not against anything else. Using only this scale, determine which is the odd one, and if it's light or heavy, in no more than 3 weighings. You know what, now that I've written it out, why not throw this out as a question to the audience, too? PUZZLE #3! It's super-old but has a neat counterintuitive solution.
Comments screened, correct answers will stay screened until I post solutions.