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Posts Tagged ‘Prime Cuts’

Listener 4660 Prime Cuts by Zag

Posted by gillwinchcombe on 12 Jun 2021

Oh my goodness this one took some solving! First, congratulations Zag on your great choice of title – another contender for best title of the year.

Prime Cuts set a record for me – 17 pages of meticulous working and an elapsed time of a week. I came to the Listener via the numericals and I enjoy solving them, but had I not been so keen, I may have been tempted to give up.

In fairness one page (but only one) of the 17 was reworking caused by a certain mathematician telling me that there were 3 pairs of reversible primes, rather than the actual 4. That sorted, it was a steady and rather strenuous uphill climb to reach the gridfill. I confess I was hoping for some sort of a revelation in the 21 letters but with all the vowels absent that was unlikely (I hope I haven’t missed it).

Without the test for triangular numbers (8n+1 gives a square number), kindly supplied by said mathematician in penance for his earlier misinformation, Prime Cuts would have taken me even longer. Still, I’m proud of finishing it and I’m glad I didn’t need to resort to the offer of Mathematika.

Thanks Zag for providing a week on and off of sustained mental workout,


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Prime Cuts by Zag

Posted by shirleycurran on 11 Jun 2021

Our first reaction is “Well the grid isn’t immense: maybe it’s not too threatening.” We read the preamble and see at once, that we are going to remove two-digit primes. A quick count tells us that there are to be twenty-one removed primes and we know there are only twenty-one two-digit ones in the primes list, so we are going to have to keep a record of the ones we remove.

Of course, I have also checked that Zag, even if he sticks with numbers, is allowed into the Elite Oenophiles set-up and he has warned us in his preamble that there are no doubles or triples “All entries are different” but there isn’t much question about what one drinks with ‘Prime Cuts’ so I suspect that we can give him the benefit of the doubt and raise a glass of vintage red. Cheers, Zag!

We know that Zag will have a unique solution and we imagine that clever solvers will have created spread-sheets to work their way through the possibilities for each of the solutions but we struggle laboriously with pencil, paper and an antique calculator and are pleasantly surprised when 3d, 15ac and 15d give us solutions and our grid begins to fill. All went well until, of course, we came to a standstill at 12ac.

But you wouldn’t be reading solvers’ blogs if you hadn’t completed the puzzle, so suffice it to say that we struggled on and luckily spotted that V had to be 67, as it was the only prime left in our list with ascending digits so that 24679 had to be the entry for 10d.

That means that 9ac can be 12 or 62 and with four primes left to extract from solutions (53, 97, 89 and 71) the final three calculations seem to offer us hundreds of possibilities. Were we just lucky or was there a short cut? 6532 worked for 6ac and we hooted with joy when calculations worked for 2ac and 4d – those two must have taken us as long as the remainder put together.

What can I say? Many thanks to Zag – we are relieved that we can solve word puzzles now for three months.

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Listener No 4660: Prime Cuts by Zag

Posted by Dave Hennings on 11 Jun 2021

The last Zag Listener was that (thankfully) rare instance of a mathematical Playfair puzzle. This week, we had to deal with numbers from which 2-digit primes needed to be removed before entry in the grid.

The starting point was 15ac where the 5-digit answer was the cube of prime D with prime L being removed to give the square of prime S. A quick examination of D from 23 (lowest 5-digit cube of a prime) to 43 (highest 5-digit cube of a prime) revealed that only D = 23 or 29 worked, with 121(67) and 2(43)89 giving S = 11 or 17. 10dn with ascending digits precluded 121(67) since it could not end in 2.

As usual, I will leave a detailed analysis of this Listener mathematical to my co-bloggers and

The enjoyable feature of this puzzle was that, using Adrian Jenkins’s The Number File, simple scanning of the entries under “Squares of integers to 100”, “The first 200 triangle numbers” and the two pages of primes, together with limited calculator checking was all that was needed. Obviously, those of you anticipating a more taxing mathematical would have been disappointed, but no doubt the next one will appease them!

Mind you, it wasn’t a particularly quick solve and my notes ran to six pages.

Thanks for a gentle quarter, Zag.

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