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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.
- Dave has a ridiculous thing:

Stupid question with not enough information from FB.

Amusing about the lack of apostrophe though. #ukedchat pic.twitter.com/fMOTefywfv— Dave Gale (@reflectivemaths) April 9, 2017

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:

My 11 year old's sample SATs papers found in his book bag. "Work out 1118÷43 (no calculator)." I wish all ministers had to take these tests. pic.twitter.com/dEOiLv2fsJ

— Rob Eastaway (@robeastaway) March 22, 2017

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 $\left(1 + \frac 1 a\right)\left(1 + \frac 1 b\right)\left(1 + \frac 1 c\right) = 2$

## 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 🙂

## Stephen Cavadino

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.