# Posts Tagged ‘Triangle numbers’

Posted by shirleycurran on 12 Mar 2021

It’s the dreaded numerical again – bound to lead to Numpty friction. We download a triangle with a hint of surprise and read through an intriguing pre-ramble where we are told that the 15 letters that appear in the clues represent the numbers 1 to 15. We jot those letters down and almost immediately see that they spell TRIANGLE and UYSMZJY which suggests to us TRIANGLE SUMZ JOY (despite the fact that we know Oyler, like one of the Numpties is a St Andrews’ alumnus and should have some inkling of how to spell ‘sums’). With I and A already in the grid, we tentatively write that around our grid and later have the joy of realizing that those pairs of digits in the perimeter are ‘triangle sumz’ – adding to triangular numbers. Nice one Oyler.

The other Numpty immediately works out that six perimeter cells will contain double digits. He spots that 14ac and 9d have to be the way into the puzzle but manages to eliminate the possibility of 731511 at 8d so is soon at his first dead-end when he opts for a solution that puts 10 at the end of that clue – where it can’t go, as it has to be the G of 2 Down Right. And so it goes, as usual with numericals until light finally dawns and peace is restored until mid May when  we’ll  get the next of these things.

Happily, I have a more rewarding task checking that Oyler retains his place at the bar and he leaves little doubt. He starts with GROG and with OIL ME two clues further down is already ‘well oiled’ before we get to his rather peculiar attempt at SANGRIA (GRANNSSANG – pretty well-oiled already but we know about his spelling!) Next he’s into the malts with TAY – we look it up and find there’s the Dalmore TAY DRAM but reading on we find he’s using a MUG and a JAR for those. It gets worse; he moves on to RUMS, before returning to the malts with ANNAN (Annandale, we suppose).

I dread to think whether the MARY in the penultimate clue is a Bloody one – it has to be! Cheers, Oyler and thanks for a numerical that wasn’t too awful.

## 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