Welcome to this week’s Math Munch!

This week we meet an incredible mathematician, take on a tough number puzzle, check out a wonderful mathematical card trick, and much more.

A while ago we shared an interview with mathematician Fan Chung Graham. The interview was posted by Anthony Bonato, The Intrepid Mathematician. Well, this week we share another of his interviews, this time with Maria Chudnovsky, graph theorist and star of not one, but two television commercials. (A rare feat for a mathematician.) Maria is also a winner of the extraordinary MacArthur “Genius” Grant. You can check out the video below or click here for the full interview.

Up next, our friends over at The Aperiodical do a lot of great things for the math world. One contribution is the monthly Puzzlebomb put on by Katie Steckles.

This month’s puzzle is MODOKU, a sort of sudoku style puzzle where columns and rows span the possible remainders mod 7 and mod 5. Check it out! Thanks to Katie for such a lovely puzzle! You can click below for an interactive version with complete instructions.

Finally this week, it’s time again to look at a Futility Closet, a phenomenal blog containing the odd mathematical tidbit. We’ll take a look at three of them.

Here’s a weird arithmetic fact I found there. Do you see what’s going on there? I have absolutely no idea how often this kind of thing is true, if ever again, but it gets me thinking.

Here’s another incredible one. We’ve posted about Pascal’s (Yang-Hui’s) Triangle lots of times (1 2), and I’ve come across a lot of fascinating stuff about it, but this is new to me. Apparently, “the product of the six numbers surrounding any interior number in Pascal’s triangle is a perfect square.” Can you prove it?

Now on to the biggie… This is such a cool card trick! Here’s the trick as explained by Futility Closet:

“I hand you an ordinary deck of 52 cards. You inspect and shuffle it, then choose five cards from the deck and hand them to my assistant. She looks at them and passes four of them to me. I name the fifth card.” !!!!!!!!!!

The key to the magic is this chart:

{low, middle, high} = 1

{low, high, middle} = 2

{middle, low, high} = 3

{middle, high, low} = 4

{high, low, middle} = 5

{high, middle, low} = 6

Can you figure out how it works from the chart alone? You’ll need a good assistant to get on board, and it wouldn’t hurt to practice a bit. Then get ready to impress. Oh, and if you can’t figure out the trick from the chart alone, then just head over to Futility Closet and read the full explanation.

Well that’s it for this week. Hope you found something delicious. Bon appetit!

Related to the “Best Card Trick”, what happen if two or more of the cards have the same value?

There is a tie breaker using suits. Alphabetical, I think.

There are a large number of “mirror multipliers.” Most are trivial (where A*B=C*D when A is a multiple/factor of B/C/D, or A & B are palindromes).

There must be a large number that have multiples of 11, 101, 111, 1001, 1011, 1101, etc.

Here are a few 2×2 digit sets.

24*63=36*42

26*93=39*62

36*84=48*63

46*96=69*64

Good stuff!

What happen if two or more cards have the same value?