## Posts tagged ‘Peter Winkler’

### Let Me Pencil You In

Pencils are infintely useful yet ridiculously simple — just a cylindrical piece of graphite surrounded by a hexagonal wooden sheath.

Well, typically.

Pencils come in all shapes and sizes, actually. They often have hexagonal cross sections, though some are octagonal, rectangular, circular, and oval.

Heck, there are even pentagonal pencils…

Which has to make you wonder, do we really need pencils in such a wide variety of shapes?

The answer may be no, but there is a practical reason for the multitude of cross sections. Can you think of any possible benefits that a rectangular pencil would have over a circular one, or vice versa?

The following problem about a pencil comes from Peter Winkler’s *Mathematical Mind-Benders*:

A pencil with pentagonal cross-section has a maker’s logo imprinted on one of its five faces. If the pencil is rolled on the table, what is the probability that it stops with the logo facing up?

And here’s a good Fermi question:

How many pencils are there in the world?

I have no idea what the answer is, but one respondent to this question on www.answers.com said, “42,462,013,000,000,000 pencils about.” The amazing part is that **17 people found this useful**!

Slightly less ambiguous is this question:

How many pencils were used to make this sculpture by George Hart?

Or maybe you prefer selected-response items…

Which of the following is the best estimate for the length of a continuous line that could be drawn using a standard pencil?

- 0.35 mile
- 3.50 miles
- 35.0 miles
- 350 miles

Or maybe you’re tired of all these questions. You didn’t come here for a quiz. You came here for some jokes. Fine.

Did you hear about the constipated mathematician?

He worked it out with a pencil.What kind of pencil?

A #2 pencil, of course!What’s the largest pencil in the world?

Pennsylvania.

If you’d like to learn more about pencils and their history — and, let’s be honest, who wouldn’t — you can **download a free copy** of Every Pencil is a Sandwich. In return, you’ll be asked to sign up for the pencils.com newsletter. If you love pencils and use them as much as I do, receiving the newsletter will be a treat, not a burden!

### Don’t Believe the HIPE

Let’s get this party started with a classic word puzzle.

What English word contains four consecutive letters that appear consecutively in the alphabet?

In *Mathematical Mind-Benders* (AK Peters, 2007), Peter Winkler describes how the puzzle above served as inspiration for a word game.

I and three other high-school juniors at a 1963 National Science Foundation summer program began to fire letter combinations at one another, asking for a word containing that combination… the most deadly combinations were three or four letters, as in GNT, PTC, THAC and HEMU. We named the game after one of our favorite combinations, HIPE.

This seemed like a good game to play with my sons. I explained the game, and then I gave them a simple example to be sure they understood.

ER

They quickly generated a long list of solutions, including:

- tERm
- obsERver
- fishERman
- buckminstERfullerene

Since that introduction a few weeks ago, the boys and I have played quite a few games. It’s a good activity to pass the time on a long car ride. The following are some of my favorites:

WKW

RTWH

RTHW

(these two are fun in tandem)HIPE

(the game’s namesake is a worthy adversary)TANTAN

The practice with my sons has made me a better-than-average HIPE player, so when I recently found myself needing to keep my sons busy while I prepared dinner, I offered the following challenge:

Create a HIPE for me that you think is difficult, and I’ll give you a nickel for every second it takes me to solve it.

Never one to shy away from a challenge, Eli attacked the problem with gusto. Fifteen minutes later, he announced, “Daddy, I have a HIPE for you,” and presented me with this:

RLF

That was three days ago. Sure, I could use More Words or some other website to find the answer, but that’s cheating. Winkler wrote, “Of course, you can find solutions for any of them easily on your computer… But I suggest trying out your brain first.”

The downside to relying on my brain? **This is gonna cost me a fortune.**

For your reading enjoyment, I’ve created the following HIPEs. They are roughly in order from easy to hard, and as a hint, I’ll tell you that there is a common theme among the words that I used to create them.

- MPL
- XPR
- YMM
- MSCR
- MPT
- ITESI
- NSV
- RIGON
- OEFF
- CTAH
- THME
- SJU
- TRAH (bonus points for finding more than one)

Winkler tells the story of how HIPE got him into Harvard. He wrote “The HIPE Story” as the essay on his admissions application, and four years later, he overheard a tutor who served on the admissions committee torturing a colleague with HIPEs and **calling them HIPEs**.

I can’t promise that HIPEs will get you into college, but hopefully you’ll have a little fun.