A delayed mathematical due to Ilver’s wonderful *Doctor Who* last week. Hopefully there are no mathematical lovers who book their holidays to avoid the penultimate Saturday of every third month… or indeed mathematical haters who book their holidays to coincide!

This week was an Oyler puzzle with two-digit primes summing to 600. I don’t know why the preamble didn’t tell us that only eight were used here. They normally do things for a reason, and I’m guessing that it was to delay the realisation that the sum of the top eight primes is 620, and in fact there are only a limited number of combinations that sum to 600 — just three, I think:

– 97 + 89 + 83 + 79 + 73 + 71 + 67 + 41

– 97 + 89 + 83 + 79 + 71 + 67 + 61 + 53

– 97 + 89 + 83 + 73 + 71 + 67 + 61 + 59

The starting point turned out to be pretty easy, with the last digits of 23ac (S) and 15dn (AS) coinciding and meaning that both A and S must end in 1. From 20dn A^S, we have 71^61 which ends 71, 71^41 also ending 41, or 61^41 ending 61. Thus A is 71 or 61 and S is 61 or 41. 12dn AA is either 5041 or 3721 and 15dn AS is 4331 or 2911, but not 2501 which results in 18ac beginning with 0.

Another point worth noting is that an even number of additions/subtractions results in an even number, while an odd number will be odd. I noted this in the top right corner of such cells, eg 5ac T+E-A ends O for odd, while 13ac R+A+W+T+E+N is E for even.

After that, things went fairly quickly for me with the long down entries at 6 WANT + REDS, 8 DREW + STAN and 9 SWAT + NERD being the last to be slotted in. It was only as I was entering the last digits of these entries that I realised the hints that Oyler was giving us, especially DREW STAN which is STAN DREW the wrong way round. So a quick check of Wiki and I find that the University of St Andrews, Scotland’s first university, was founded in 1413, so that date went in at 1ac and 2013 at 31ac.

The values of each letter were A = 71, D = 79, E = 89, N = 73, R = 83, S = 41, T = 67 and W = 97.

The symmetrically hidden versions of the dates didn’t take long to find since it was a dead giveaway that the two lines would be the diagonals representing the white cross on the Scottish flag. I drew them in, but they were a bit of a puny version of the flag which the animation shows up better. (I forgot to take a copy of my submission, so no little insert this week.)

What a nice coincidence it was, not only that the 50th anniversary of *Doctor Who* appeared on a Saturday but that it could nudge the usual occupant of that penultimate Saturday to a 600th anniversary slot the following Saturday, St Andrew’s Day. Was it Ilver, Oyler or one of the editorial team. Whoever it was, it finished off a superb couple of puzzles, so thanks to all involved.