# Posts Tagged ‘roundabout sums’

## Listener No 4647: *Roundabout Sums* by Oyler

Posted by Dave Hennings on 12 Mar 2021

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## L4647 ‘Roundabout Sums’ by Oyler

Posted by Encota on 12 Mar 2021

We always expect something interesting when Oyler’s name is attached to a numerical – and this was no exception! My thanks to *Oyler* for what I managed to make a trickier puzzle than it probably needed!

I read the Preamble – the bit about ‘Some perimeter cells will contain two digits’. I then – stupidly with hindsight – asked myself whether this told me that all other cells in the puzzle contain *exactly* one digit? Unfortunately for me, I decided that it *didn’t* tell me that. The ‘literal’ bit told me that the numbers 1 through 15 were most likely to appear in the fifteen edge cells – but what about the central ones?

Luckily some clues helped me out a bit – eg 7dr had to be two digits long and so have one in each cell. Similarly 9dl had to have four digits, one per cell. Bit by bit I crept around the grid, identifying cells which had to have just one digit in them and eventually I cracked it. Of course, once I saw there was no possibility or need for any of the central cells to contain more than one digit *then* I knew that the simpler reading of the Preamble would have sufficed!

That made it a very enjoyable solve, even though I appear to have added an entirely unrequired additional layer of complexity. Or maybe that was intended? My guess is No!

With the help of OEIS (sequence A020756, I think) I managed to confirm that all pairs of joined number-strings round the perimeter were triangular, which seemed quite impressive, given it all linked up back round to the start. My instinct is that such a sequence must be fairly uncommon, though I didn’t explore this further.

That left TRIANGLE SUMZ JOY around the edge, when taken ‘literally’, which was reassuring that I must have (at least) most of the puzzle correct.

Oyler has also hinted, with a Title including “Roundabout” and 8ac beginning “Yes” to a Prog Rock under-theme that elsewhere we’d perhaps be more likely to see from the setter Moog! I did wonder, for a moment, if that much later album from Yes entitled ‘90125’ was also going to feature. Apparently No – unless I’ve made a mistake (quite possible!)

Thanks again Oyler!!

Cheers & stay safe all,

Tim / Encota

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