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I see, Meursault, so the numerics are a sort of tie-break for the competitive among us. Thanks for the background. I only ever pick up the Listener when I'm visiting my parents on a weekend. I think I shall hope to avoid the four in a year - a one in 13 chance every time. I can live with that...

This won't mean I start visiting less often, Mum, I promise...

Hi, mdmaylwin,

The numerical puzzles normally appear on the third Saturday of February, May, August and November, so if you avoid these weekends for your visits, you will be safe.

Thanks Mersault for the tips regarding the NW corner. However I have another dilemma. I can only resolve 35A as being a type o clue, but the numbers I have entered for the crossing entries 22D and 32D mean there is no number of type o that can fit for 35A. Am I in error thinking that 35A is a type o?

Goshawk, 35a is a type m clue, not type o. The three type m clues were mentioned earlier in the forum: 34, 35, 38
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mdmaylin: mersault. the mathematicals weren't 'thrown-in' as you say by the editors. They have been around since 1932 with puzzle number 111 and that got the highest entry of the puzzles 1 to 111. So solvers of The Listener Crossword have been used to having to solve mathematical puzzles for a long time if they wish to be in with a shout of the SSS, Solvers Silver Salver.

Oops. Realised that 35A is in fact property m.

Hmmm. Third weekend in May is my brother’s birthday; third in August the annual holiday in a Devon. This could prove controversial...

Just to complicate things, the numerical Listener normally appears on the penultimate Saturday of the month, so once in a while it could be the fourth Saturday if there were 5 in the month - August next year for example. Also the pattern is occasionally upset if there is a Listener themed on a particular anniversary etc.
Be warned, the Listener is addictive.

I’m in the possible minority that look forward to the numerical as a change from the crossword. I think 4 a year is about right.

I really enjoyed the first bit of this, thought it was a clever idea to have to allocate the clue numbers to the properties. The problem, as others have said, is that I ended up having to resort to spreadsheets to finish the puzzle.

I always try to solve completely manually, with no calculator or spreadsheet, and have solved a few numericals this way. Normally I resort to a calculator if there are a lot of possibilities that I need to check, and I don’t mind this. But trying to find a 5 digit tetrahedral number from 40 possibilities in a reasonable time seems to me to be only possible using a spreadsheet, which is what I did, as did many others by the sounds of things. I always find this disappointing. If anyone out there has a way to do this without using a spreadsheet, I’d be interested to hear how.

Hi, smellyharry,

I don't think that there is any particular virtue in not using tools such as spreadsheets for numerical puzzles like this. For this puzzle, I also made use of online lists of prime numbers (particularly useful for the answer to 37, a five-digit prime). I prepared a spreadsheet list of diagonal numbers for property o and tetrahedral numbers for property h, and also for sums of two non-zero squares, so didn't bother with the prime factorisation approach suggested by the preamble. Some other online lists, such as Fermat and Mersenne primes, were useful.

I'm more relaxed about using spreadsheets for numerical puzzles than using anagram solvers and similar tools for word-based puzzles, but I must admit that I sometimes make use of these aids when stuck.

The thing I find most helpful is to write down every step of my reasoning, so that, if I run into contradictions or dead ends, I can go back and spot where I went wrong.

Although on my first run through this puzzle, I associated properties with clue numbers as I went, I did a second run and found that I could associate all but eight clues with a specific property (allowing for the two properties associated with 10 and with 23) without actually solving any of the clues. I'm not sure that this was much quicker than the more ad hoc approach, but I think the logic is more elegant.