The Collatz Conjecture via Mathpickle

Unbeatable! Combining a Greek myth with an investigation with a reward attached!

We start our investigation of patterns every year with this contest offered by Mathpickle:

http://mathpickle.com/project/daedalus-and-icarus-try-to-escape/

We start with any youtube video of the tale of Icarus. Then we show the video from mathpickle (link above). They claim to be offering a $1,000,000 prize to any child who can find a number that does NOT end with one when we follow these 2 rules: RULES: Choose any number.

  • If the number is even, divide by 2.
  • If the number is odd, multiply by 3 and add 1. Repeat until the chain works its way down to ONE.

Talk about a buzz! IMG_9790

What we appreciate about this activity is that everyone can get into it, and it involves a practice of multiplication and division that is fairly painless.

 

Some students got IMG_9793-3277969482-1540011972972.jpg so excited  (partly by the challenge, partly by the prize money!) that they stayed in at lunch and tried larger and larger numbers.

 

 

A group of 3 are still coming, day after day, chipping away at the problem.

Here are 2 significant insights:

  • In order to end with ONE, every number must at some point go to a power of 2. (This lead to an investigation of binary numbers, in case they might hold the key to figuring this out)
  • All the powers of 2 they’ve investigated are preceded by an ODD number that end in  one or five! (Something I’ve never noticed before!)

They’re set on continuing this challenge – we’ll keep you posted!

IMG_9807.JPG

Of course the powers of 2 descend to 1, but the numbers BEFORE that are odd, and can only be odd. And only every OTHER power of 2 works, and the odds show a pattern of 1, 5, 1, 5, 1, … in the ones place!

We’ll keep you updated!

ODD:      POWER OF 2:

341 ->        1024

512

85 ->          256

128

21 ->          64

32

5 ->            16

8

1 ->            4

2

1

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