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Resources tagged with Dynamical systems similar to Sperner's Lemma:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

There are 15 results

Broad Topics > Sequences, Functions and Graphs > Dynamical systems

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Whole Number Dynamics II

Stage: 4 and 5

This article extends the discussions in "Whole number dynamics I". Continuing the proof that, for all starting points, the Happy Number sequence goes into a loop or homes in on a fixed point.

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Whole Number Dynamics III

Stage: 4 and 5

In this third of five articles we prove that whatever whole number we start with for the Happy Number sequence we will always end up with some set of numbers being repeated over and over again.

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Recent Developments on S.P. Numbers

Stage: 5

Take a number, add its digits then multiply the digits together, then multiply these two results. If you get the same number it is an SP number.

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Whole Number Dynamics I

Stage: 4 and 5

The first of five articles concentrating on whole number dynamics, ideas of general dynamical systems are introduced and seen in concrete cases.

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Whole Number Dynamics IV

Stage: 4 and 5

Start with any whole number N, write N as a multiple of 10 plus a remainder R and produce a new whole number N'. Repeat. What happens?

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Try to Win

Stage: 5

Solve this famous unsolved problem and win a prize. Take a positive integer N. If even, divide by 2; if odd, multiply by 3 and add 1. Iterate. Prove that the sequence always goes to 4,2,1,4,2,1...

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Dalmatians

Stage: 4 and 5 Challenge Level: Challenge Level:1

Investigate the sequences obtained by starting with any positive 2 digit number (10a+b) and repeatedly using the rule 10a+b maps to 10b-a to get the next number in the sequence.

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Difference Dynamics

Stage: 4 and 5 Challenge Level: Challenge Level:1

Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?

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More Beads

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

With red and blue beads on a circular wire; 'put a red bead between any two of the same colour and a blue between different colours then remove the original beads'. Keep repeating this. What happens?

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Sums and Products of Digits and SP Numbers

Stage: 5

This article explores the search for SP numbers, finding the few that exist and the proof that there are no more.

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Difference Dynamics Discussion

Stage: 5

This article discusses what happens, and why, if you generate chains of sequences getting the next sequence from the differences between the adjacent terms in the sequence before it, eg (7, 2, 8, 3). . . .

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Number Chains

Stage: 5 Challenge Level: Challenge Level:1

Find all the periodic cycles and fixed points in this number sequence using any whole number as a starting point.

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Take Ten Sticks

Stage: 4 Challenge Level: Challenge Level:1

Take ten sticks in heaps any way you like. Make a new heap using one from each of the heaps. By repeating that process could the arrangement 7 - 1 - 1 - 1 ever turn up, except by starting with it?

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Odd Stones

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

On a "move" a stone is removed from two of the circles and placed in the third circle. Here are five of the ways that 27 stones could be distributed.

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Spiroflowers

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Analyse these repeating patterns. Decide on the conditions for a periodic pattern to occur and when the pattern extends to infinity.