Oakwood's Mathematicians and the Collatz Conjecture...
Some able mathematicians in Years 5 and 6 have been working on a very old number problem. They didn't get any instructions, just this cartoon by Randall Munroe:
The Hungarian mathematician Paul Erdős said "Mathematics is not yet ready for such confusing, troubling, and hard problems," but Oakwood's mathematicians were!
They had to work out what was happening before they could work out what to do! Can you work it out? (See the answer below if you can't!*)
The problem is called the Collatz Conjecture and was orginally suggested by Lothar Collatz, a German mathematician, in 1937.
Nathaniel, Aaron and Isaac in Year 5 worked out the rules for each step and then tried the rules starting with the number 27. They found all 111 steps by working it out accurately on big sheets of paper (click on the picture to see a big version!)...
They then put all their data into Excel and graphed their results. Starting with 27, they found that the rules took them as high as 9232 before coming back down to 1...
(*Starting with any number, if it's even, halve it, if it's odd, multiply it by three and add one. Carry on following the same rules on each answer you get. If you get to 1, stop...)
2 comments:
Always enjoyed this sort of problem when I was at school. Well done Nathaniel, Aaron and Isaac.
This has puzzled me since I saw you all working on it...I understand it now and am amazed at how you have worked it out! Bring on the next problem please!
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