# Wrong, But Useful: Episode 43

In this month's installment of Wrong, But Useful, our special guest co-host is @mathsjem (Jo Morgan in real life) from the indispensable resourceaholic.com.

• We start by talking about resourceaholic.com and how Jo manages to fit such a punishing blog schedule around being a nearly-full-time maths teacher.
• Colin wonders how writing has affected Jo's teaching practice.
• The number of the podcast is 530, an untouchable number.
• Apparently you peasants who carry money around are excited about the new £1 coin. Jo used to work at the Bank of England and has insights about how statistics can be applied to the circulation of banknotes. We refer to an article by @mscroggs about £1 coins. Dave denies ever having walked out of the Bank of England with 20 one-pound coins in his shoes – but then, he would. We discuss counterfeiting.

A threepenny bit

• Dave has a ridiculous thing:

We refer to my fake maths post.

• Dave's student answered "Simplify $7a + 5b + 3a – 2b$ with $10A + 3b$. Should they get the marks?
• @robeastaway also has a ridiculous thing:

We agree that prescribing methods is wrong.

• Colin mentions @robjlow's post on quadratics
• We discuss the effects of the new GCSE and A-level on uptake. This involves a shout-out to @stecks and @peterrowlett's Taking Maths Further podcast
• Last month's puzzles: @chrishazell72 gets a gold star for a mean of 250.5 for Christian’s 1000 means puzzle, and says that getting 10 $\frac 1 3$ chances in a row over 100 trials is about 1/1000
• This month: a square has an area of 18. What’s its diagonal? Also, Find all triples of positive integers $(a,b,c)$ such that $\left(1 + \frac 1 a\right)\left(1 + \frac 1 b\right)\left(1 + \frac 1 c\right) = 2$

## Colin

Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.

### 3 comments on “Wrong, But Useful: Episode 43”

• ##### Sam Steele

Dear Mr. Beverage and Mr. Gale,

The first puzzle is easy.
I got 6 (root 2 × root 18).

The second is interesting. I got 3, 4 and 5 quickly enough. Then (before I noticed that it was positive integers only) I got -9, 2 and 2.

I cheated and wrote a little program, and it seams that, ignoring permutations, there are only 5 answers:

2, 4 and 15
2, 5 and 9
2, 6 and 7
3, 3 and 9
3, 4 and 5.

I can’t work out why there are only 5.
Perhaps you will tell us why, next month.

Yours sincerely,

Loyal listener, Sam Steele, Carrum Downs, Australia.

• ##### Colin

Thanks, Sam! I’ve not done the puzzle yet, but we’ll be sure to send a star your way 🙂

Re Square Question – sides are rt 18, which simplifies to 3rt2. Hence diagonal is 3rt2 x rt2 = 6

The other one will take more thinking.