Please feel free to ** contact me **.
This pages hosts a few short notes on topics from recreational mathematics.

### Sylvy's mathsy blog

Here is a link to my blog **sylvy's mathsy blog**, which has the slogan `my blog, mostly Maths'.

### Sylvy's puzzle corner

#### $\vdash$ latest puzzle

#### $\vdash$ older puzzles

### miscellany of fun maths

### outreach talks

- puzzle #19: A tribute to Rubik's Cube

- puzzle #18: Quick Pythagoras
- puzzle #17: Lanbot's Logic Puzzles, courtesy of the Lancashire Science Festival
- puzzle #16: Sections through a cube
- puzzle #15: Optimist, Pessimist
- puzzle #14: Heptagon
- puzzle #13: Pentagon
- puzzle #12: coming soon!
- puzzle #11: All present and correct
- puzzle #10: Round and round (coming soon)
- puzzle #9: Long Division (solution)
- puzzle #8: (coming soon)
- puzzle #7: Factorial, Factorialer, Factorialist
- puzzle #6: the puzzle forest (solution)
- puzzle #5: vertex of parabola
- puzzle #4: continuum chain in $\mathcal{P}(\mathbb{N})$ (solution)
- puzzle #3: Sonic topology (solution part (i), solution part (ii))
- puzzle #2:
**magic number**

Your task is to identify the*smallest*positive whole number $N$ with the two following properties.- $N$ has exactly $144$ factors (including itself and $1$).
- Among the factors of $N$ there are at least $10$ consecutive numbers.

- puzzle #1:
**coin tossing**

This problem is about tossing coins,**H**denotes a Head and**T**denotes a Tail.

- Anne tosses a fair coin twice. What is the probability that she obtains
**HH**? - What is the probability that she obtains
**HT**? - Next, she plays a different game. She repeatedly tosses the same fair coin until she obtains
**H**. What is the 'average' (i.e. expected) number of tosses this will take?

In games of this kind, she repeatedly tosses the same fair coin until a certain pattern comes up. For example, if that pattern is**HH**then she keeps tossing the coin until the two most recent tosses have both been Heads.

- What is the expected number of tosses when she is seeking the pattern
**HH**? - Finally, what is the expected number of tosses when she is seeking the pattern
**HT**?

- Anne tosses a fair coin twice. What is the probability that she obtains

- Reasoning: Knights and Knaves Puzzles
- Reasoning: Pirates and coins
- Analysis/Probability: Coloured balls in jar
- Analysis: A 'mean' question about the sequences of Cesàro means
- Analysis: A fun question about the convergence of series
- Analysis: Tricky Questions, Problem Sheet 1 about convergence and continuity
- Strategy/Set Theory: Hat problems (joint work with Rob Leek)
- Euler characteristic, graphs, solids
- Tennis
- Kittens
- naive calculus
- non-Euclidean geometry
- Rigid structure of Platonic solids, lengths, areas, and volumes
- colourings of solids
- Spinning Platonic Solids
- Conic sections
- Four switches, levers
- Hairy Ball Theorem
- Pancake Theorem, Red and blue points on the plane
- Permutations with jam
- Homogeneity, random graph, $(\mathbb{Q},<)$, back-and-forth

- Puzzles: Hats, hats, and more hats, open day talk, 2018.
- Special Relativity: Space, Time, and Relativity, talk for schools, 2017.
- Puzzles: Hats, hats, and more hats, applicant day talk, 2017.
- Set Theory: Three Portraits of Infinite, talk for schools, 2016.
- Logic: Logic, Puzzles, and Gödel's Incompleteness Theorems, talk for schools, 2014.
- Set Theory: Cantor's Infinities, talk for schools, 2011.