Crossing the bridge.

Four people need to cross a rickety rope bridge to get back to their camp at night. Unfortunately, they only have one flashlight and it only has enough light left for seventeen minutes. The bridge is too dangerous to cross without a flashlight, and it’s only strong enough to support two people at any given time. Each of the campers walks at a different speed. One can cross the bridge in 1 minute, another in 2 minutes, the third in 5 minutes, and the slow poke takes 10 minutes to cross. How do the campers make it across in 17 minutes?

Solution in comments.

The Mathematics of Sharing Pizza

When several hungry but cash-challenged college students chip in for a pizza, cutting it into equal and fair slices become very important. So important that mathematicians Rick Mabry and Paul Deiermann looked into the problem that emerges when the pizza cutter does not slice exactly through the center of the pie. This is known as the complete pizza theorem.

Their quest started in 1994, when Deiermann showed Mabry a revised version of the pizza problem, again published in Mathematics Magazine (vol 67, p 304). Readers were invited to prove two specific cases of the pizza theorem. First, that if a pizza is cut three times (into six slices), the person who eats the slice containing the pizza’s centre eats more. Second, that if the pizza is cut five times (making 10 slices), the opposite is true and the person who eats the centre eats less.

Only the first statement was proven. Deiermann and Mabry worked on proving the second off and on until their breakthrough in 2006. Now that they have proven the theorem, they are working on other problem, such as how to divide a calzone.

More information: link
Story taken from Neatorama

Möbius Bagel

George Hart is a sculptor, mathematician, and one of the best professors I had while at Stony Brook University. Never failing to amaze me, he has posted on his website step-by-step instructions for how to craft a Möbius strip from a single bagel.

“It is much more fun to put cream cheese on these bagels than on an ordinary bagel. In additional to the intellectual stimulation, you get more cream cheese, because there is slightly more surface area.”

This makes me miss seeing George every Tuesday and Thursday for algorithms!

More information: link

Wolfram|Alpha

Have you ever given up working on a math problem because you couldn’t figure out the next step? Wolfram|Alpha can guide you step by step through the process of solving many mathematical problems, from solving a simple quadratic equation to taking the integral of a complex function.

This looks like it could be fun!

More information: link

Puzzles!

I just put a couple of puzzles up in the content section; a number game, my Rubick’s cube solution, and a logic problem. I’ve got some cleaning up to do, but at least it’s up there to play with! Have a look and have some fun!

This just made my day:

This check is for $536.49

Will do math for work.

Haha, I love this!

Mathematical proof that girls are evil.

I’ve always loved this, so I figured I’d just put it into text here for anyone that hasn’t seen it before!

Proof that girls are evil:

First, assume that girls will require time and money.
girls = time × money

We all know that “time is money.”
time = money

Therefore:
girls = money × money
girls = (money)²

And because “money is the root of all evil”, we know that:
money = √‾evil

Therefore:
girls = (√‾evil)²

The square simply cancels the square root and we are left with:
girls = evil

end of proof.

mid-semester

I have been so busy the past few weeks I haven’t had time for anything! Things have calmed down a bit for the time being, but I know it won’t last too long! I’m just heading to bed but I wanted to at least keep things interesting here and post a math problem! A little combinitorics, so have fun with it! Solution is in the comments!

A bracelet is made by threading 4 identical red beads and 4 identical yellow
beads onto a hoop. How many different arrangements of the 8 beads can be made?

Just another weekend.

This weekend I went and watched Burn After Reading and read The Last Lecture by Randy Pausch, both of which I enjoyed greatly! I recommend them both. School is back in full swing and I am slowly losing all of my free time again; I miss it already. But, there is the light at the end of the tunnel: Only 8 months until graduation. I guess it is time to start thinking about what comes next; not something I really want to get into right now.

I guess I’m kind of distracted right now by football (Dallas/Philadelphia, hell of a game by the way) and I feel like I’m being short. So, I will leave this with a math problem:

When we perform a ‘digit slide’ on a number, we move its units digit to the front of the number. For example, the result of a ‘digit slide’ on 6471 is 1647. What is the smallest positive integer with 4 as its units digit such that the result of a ‘digit slide’ on the number equals 4 times the number?

Solution is in the comments