We’ve recently had some kitchen improvements, so we now have a nice shiny stainless steel sink. We’re rather proud of it, but what no-one told us is that even the top-range models are so sensitive that they take offence if you don’t speak nicely, or if you forget to wish them good morning in an agreeable manner.

Consequently, within five minutes the first scratch appeared. True it was invisible to all but high-powered lighting and advanced microscopy, but I was at the hardware store buying a sink mat moments later. The sink mat worked very well but it really didn’t look state-of-the-art, and a couple of weeks later we were in a kitchen shop and found something rather more interesting.

We’d discovered a device called a SinkSaver^{TM}. The basis of this is that the designer has said that the business area of your sink can be thought of as a 3×3 square. One of the nine cells will be the drain area, so there are eight cells which the Sinksaver needs to protect.

The problem for the designer is that different models of sink have the drain in different positions. Sometimes the drain is at a corner, sometimes in the centre, and others – like ours – have the drain in the middle of one side. So the designer has produce a device which is made of two separate sections which can be clipped securely together to accommodate the drain in any one of the three possible positions.

You can find out more at https://www.josephjoseph.com/en-gb/product/sink-saver/ – but before you do that, can you work out the shapes of the two sections?

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Clever!

You can reason the solution out. The first line of attack is that the two sections should have four squares each, but the T-shape and the 2×2 square both fail because the central square can’t be left uncovered. The 1×4 strip isn’t worth considering, and the L shape doesn’t work either. So we have to consider a 5-square with 3-square solution, and you soon eliminate all the 5-square possibilities apart from the L-shape. Incidentally, there’s a connection with another post that’s in the pipeline, but this one doesn’t involve our kitchen.

I haven’t seen the other post. I really like how state-of-the-art, practical and mathematical the manufacturer made them and their instructions .

The invention – and seeing the maths potential in it – are great! It reminds me about a sort of problem I got interested in when I started playing with our Cuisenaire trays earlier on in the year:

http://followinglearning.blogspot.fr/2015/01/cuisenaire-squares.html

Also linked in, I’ve just learnt about polyomino number theory, from Paul Salomon via Twitter, eg:

http://www.paulsalomon.com/math.html

with the idea of polyomino factors:

https://cms.math.ca/crux/v28/n3/page147-150.pdf

Wow, wow, wow! There are truly amazing people and amazing discoveries out there. The Cuisenaire questions alone seem immensely rich, and I can’t ever recall seeing them raised previously.

I suppose a question that comes out of this is… are all sinks 2-savable?

(But it’s Monday morning and the start of term, so I mustn’t think about that now!)

Looks like a sink survey is called for. Ours certainly looks as if an optional 3×1 extension would be useful, and when I measure, I find the sink measures 435mm by 350mm, which is very close to a ratio of 1.25:1 On the basis of this rather small sample, the golden ratio doesn’t apply to sinks – do please consult your pupils!