Articles by rychardemanne

A Tribute To Richard Feynman: Feynman Point Pilish Poems 2013

rychardemanne — Fri, 10 May 2013 23:56:41 +0000

A Tribute To Richard Feynman: Feynman Point Pilish Poems 2013

Richard Feynman was born on 11 May 1918. Today would have been his 95th birthday. This isn’t a paean to a physicist – it could be, but I’m sure millions of words have been published on this – but a game for wordsmiths and numberphiles.Within the highly restricted format of the Pilish Poem, the aim is to be both enlightening and eloquent; plus to have some fun playing around.You can follow my train of thoughts at my first article on this so, without repeating myself, I’ll jump right in with the basic rules of what constitutes a Feyman Point Pilish Poem.

rychardemanne Fri, 05/10/2013 - 19:56

Categories

Random Thoughts

The Math-e-Monday Puzzle: Squares from a Tetrahedral Die

rychardemanne — Wed, 08 May 2013 06:59:05 +0000

The Math-e-Monday Puzzle: Squares from a Tetrahedral Die

It isn’t Monday, but I’m puzzled every day of the week.Alice is puzzled too; she’s playing with a new tetrahedral die. Each face has a different positive integer on it, but the numbers are peculiar. Alice quickly notices that if she rolls the die and adds up the numbers on the three exposed faces, she always comes up with a perfect square. “That’s clever!” thinks Alice. Assuming that Alice’s tetrahedral die uses the smallest possible numbers, what is the sum of the numbers on all four faces?

rychardemanne Wed, 05/08/2013 - 02:59

Categories

Mathematics

The Math-e-Monday Puzzle: Infinite Packings Within Finite Figures

rychardemanne — Tue, 09 Apr 2013 00:46:22 +0000

The Math-e-Monday Puzzle: Infinite Packings Within Finite Figures

After the scramble to get out of jail, here are some questions about imprisoned shapes! In my last question, we came across parts of the so-called harmonic series 1/2 + 1/3 + 1/4 + 1/5 ... 1/n. Now, this series is divergent; it does so very slowly, but as n tends towards infinity so does the sum. However, the sum of the squares of each term is convergent.So, numerically, if we add together the areas of squares with sides of 1/2 units, 1/3 units and so on, we will tend towards a finite limit. However, is it possible to geometrically fit these squares inside a square of 1 unit side without any of them overlapping?

rychardemanne Mon, 04/08/2013 - 20:46

Categories

Mathematics

Solution to The Jailer's Revenge

rychardemanne — Mon, 08 Apr 2013 11:30:37 +0000

Solution to The Jailer's Revenge

The solution to the Jailer’s Revenge question is fairly lengthy, so I think it warrants a separate blog entry. Please refer to the original question as it too is fairly long.Let’s firstly simplify the problem with smaller numbers, then scale it back up to 100 lockers and 100 prisoners. Let’s start with just 10 lockers and 10 prisoners.

rychardemanne Mon, 04/08/2013 - 07:30

Categories

Mathematics

The Math-e-Monday Puzzle: A Jailer's Revenge

rychardemanne — Mon, 01 Apr 2013 09:23:34 +0000

The Math-e-Monday Puzzle: A Jailer's Revenge

This is a fairly new problem, being traced back to as recently as 2003. However, it also has the kind of counter-intuitive solution that has made it a favourite on mathematical websites and forums. In its various retellings, it sometimes suffers from a lack of stringent conditions that result in rather imaginative solutions; perfectly legitimate solutions within the parameters set but not always the ‘classic’ one. If you’ve seen this before, then speed-read to the end where we take the side of the jailer!The problem

rychardemanne Mon, 04/01/2013 - 05:23

Categories

Mathematics

The Feynman Point And Pilish Poetry

rychardemanne — Fri, 29 Mar 2013 21:44:25 +0000

The Feynman Point And Pilish Poetry

When I was a kid, I would happily play around with both words and numbers – I still do. Both have their aesthetic appeal. Whether it is constructing and deconstructing mathematical puzzles or cryptic crosswords, they appear as small artefacts that reveal a grander architecture. Combine this with the serendipity of the internet, and Pi Day was just a hop, skip and jump away from Richard Feynman and pilish poetry.

rychardemanne Fri, 03/29/2013 - 17:44

Categories

Random Thoughts

The Math-e-Monday Puzzle: Polygons in Rings

rychardemanne — Mon, 25 Mar 2013 09:13:01 +0000

The Math-e-Monday Puzzle: Polygons in Rings

The diagram below shows five concentric circles constructed in such a way that the area of each annulus is equal to that of the central circle. Within the first annulus, a square has been constructed such that none of the points on the square lie outside the inner or outer radii of that ring. For the first annulus, A(1), with radii r(1) and r(2), n=4 is the minimum value of n such that a regular n-gon lies wholly within or on the boundary of A(1).Find the smallest value of n, such that a regular n-gon will not fall outside the annulus A(m) bounded by r(m) and r(m+1) for values of m = 2, 3 and 4.Also, what is the smallest value of n for A(50)?

rychardemanne Mon, 03/25/2013 - 05:13

Categories

Mathematics

The Math-e-Monday Puzzle: Weird Dice

rychardemanne — Sun, 17 Mar 2013 22:45:16 +0000

The Math-e-Monday Puzzle: Weird Dice

Alice wants to play a game with Bill. She has just bought some new and rather strange dice. The average of each die is 3.5, just like a normal playing die, but the numbers on each face have an unfamiliar distribution.Die P has the numbers 3, 3, 3, 3, 3, 6.Die Q has the numbers 2, 2, 2, 5, 5, 5.The game itself is very simple: whoever rolls the highest total wins a sweet from the candy box. If the box becomes empty, the winner can take one from the other player’s pile.

rychardemanne Sun, 03/17/2013 - 18:45

Categories

Mathematics

The Math-e-Monday Puzzle: Peculiar Periodic Numbers

rychardemanne — Mon, 11 Mar 2013 08:09:04 +0000

The Math-e-Monday Puzzle: Peculiar Periodic Numbers

Let N be a non-zero natural number composed of n digits. Let us then both prepend and append the number 4 to create two new numbers, 4N and N4, that are both (n+1) digits long. For example, if N is 123, then we create two numbers: 4123 and 1234.The question is to find the smallest value of N, such that the following equation holds true:4N = 4*N4Again, using the example above, this would require that 4123 = 4*1234. This is obviously not true, so N=123 is not a solution.So, find the smallest value of N and its length n.If that was too easy, can we generalise the problem? Let K be our single-digit number, between 1 and 9 inclusive, such that KN = K*NK has a solution number N.

rychardemanne Mon, 03/11/2013 - 04:09

Categories

Mathematics

Solution to Five Circles Stuck in a Triangle

rychardemanne — Sun, 10 Mar 2013 23:29:46 +0000

Solution to Five Circles Stuck in a Triangle

The "Circles Stuck in a Triangle" problem I posted last week had a rather surprising solution to it. So much so that I had to rewrite the question so that text and diagrams made sense! So here is a complete solution to what ended up being two problems; similar but different.The solution has three steps: firstly, we need to find the relationship between the three radii; then there is a bit of number theory to find explicit numbers for a and b; and finally, some trigonometry to calculate the area of the large triangle.The c=4 case

rychardemanne Sun, 03/10/2013 - 19:29

Categories

Mathematics