## Archive for March 29, 2012

### Grin and Parrot!

There aren’t too many math humorists in the world, and, for a very brief period of time, I was in high demand. (Relatively speaking, of course.) A talent agent once saw me give a presentation called *Puns and Puzzles*, which mixes number tricks with math jokes. After the show, he told me about a cruise line that caters to a very intellectual audience, and he asked if I’d be willing to perform on a ship. A month later, I was sailing the seven seas and, occasionally, making people laugh.

Aboard the *Princeps Mathematicorum*, audiences were generally polite. But one night, a rude mathematician sat in the front row with an even ruder parrot on his shoulder. Halfway through my act, I presented the following puzzle:

- Look at the 16 digits from one of your credit cards. Create two eight‑digit numbers, one consisting of all the digits in odd positions (that is, the first, third, fifth, and so on), the other consisting of all the digits in even positions (second, fourth, sixth, and so on).
- Add the digits of the first eight‑digit number, and double the result. Write it down.
- Add the digits of the second eight‑digit number. Write it down.
- How many of the digits in the first eight‑digit number are 5 or greater? Write it down.
- Now add the results of steps 2, 3, and 4.

I then magically revealed the last digit of each audience member’s result.

The mathematician rolled his eyes at the trick, and the parrot squawked, “This is just the Luhn system — brrrraaaaaak! — for credit cards! Of course the result will be 0!”

His outburst surprised me. I don’t like when my secrets are revealed. I was frustrated, but there was little I could do. It’s not like I could have an argument with a parrot. The rest of the show went poorly, and I left the stage distraught.

The next night, I had another show. But the mathematician and his bird were back, once again seated in the front row.

Wanting to avoid a repeat, I used a different puzzle:

- Take a four‑digit number.
- Scramble the digits to form a different four‑digit number.
- Subtract the smaller number from the larger number.
- Now, take the digits of the result, and add them together.

I then showed the following chart and magically predicted the symbol that would be associated with each audience member’s result:

The parrot shrieked, “Of course it will be omega! Any two numbers created from the same digits — brrrraaaaaak! — will be congruent modulo 9! The sum of the digits will always be a multiple of 9.”

Once again, he ruined my trick. I was angry, and I went to bed that night completely dismayed. But my dejection was short-lived — during the night, we hit an iceberg, and the boat sank.

I was submerged into freezing cold water. A piece of the deck was floating on the surface, and I pulled myself onto it. To my dismay, the parrot was perched on the other end. I shot him an angry look. He said nothing. I said nothing. We floated for several hours in silence, shivering, just staring at one another.

Finally, he spoke.

“Okay,” he said, “I give up. How the hell did you make the ship disappear?”