# Posts Tagged ‘Property Management’

## ‘Property Management’ by Smudge

Posted by Encota on 8 Jun 2018

Crikey, Listener 4503 was tricky, wasn’t it?  I eventually succumbed to writing a few of those functions that I had always meant to for years, for future numerical puzzle-setting.  You perhaps know the sort: isprime() to test if the number in brackets is prime and so on.  The functions  istriang() and isdiag() soon followed.  Did it help much here?  Probably not.  In fact the most re-usable one was getdigit(number, digit) to let me select any single digit within a number e.g. to compare it with another, check if it is odd, …

My suspicion is that many seasoned numerical setters and solvers must have some of these at their fingertips and more than likely a lot more – though this was the first puzzle that finally encouraged me.

I think it was about Sunday lunchtime when I finally cracked L4503, having eventually used the final 5 lines of the Preamble for the first time to determine whether my LOI at 26ac should be 522 or 524.

I was left with the worrying suspicion that their surely must have been a much more straightforward Solution Path than mine.  The Mersenne primes helped get an initial toehold but some of the properties – especially for me ‘f’ and ‘i’ – seemed to give little info until right at the end.

But I did think that the hidden message telling us to indicate those different ways to reach that special number 4503 was good.  There were, I think:

• 19 x 3 x 79
• 57 x 79
• 19 x 237 and even
• 18012 / 4

Unbelievably well hidden, I hear you say.  My finished article therefore looked like this:

What was that?  You didn’t spot the hidden message??

Cheers

Tim / Encota

Posted in Solving Blogs | Tagged: , , | 1 Comment »

## Listener No 4503: Property Management by Smudge

Posted by Dave Hennings on 8 Jun 2018

Well, this quarter I was actually geared up for this quarter’s mathematical puzzle — so often they catch me by surprise. However, I wasn’t geared up for the setter. Having expected Nod or Zag to make a reappearance, I was faced with Smudge, and he didn’t ring any bells regarding a previous puzzle. I was surprised, therefore, to find that he had set one of the tough puzzles of 2016 over two years previously — No 4388 Cycle 20% More, all about Gilbert and Sullivan’s The Grand Duke, not a mathematical at all.

This week, we had a series of properties in a list, such as square, cube, triangular number, Fermat prime. Each grid entry had to be associated with exactly one of these properties, as did the clue number at which it was entered. We were also provided with information about numbers divisible by their reverse, perfect numbers and integers which are the sum of two squares, all of which “may be helpful”.

I loved the clueing technique here, similar in many ways to Piccadilly’s The Properties of Numbers — II last year. I made a list of the clue numbers and then went through annotating each to show which of the given properties applied to them. I gradually teased out some grid entries but, two hours later, I reached a dead end — my first. This was, I think, because I had put 56 as a definite for 10dn, rather than just a possible.

I decided to be a bit more organised on my second attempt, and created a grid with clues down the left and properties/occurrences across the top:

This made it much easier to tick off the entries as I resolved them or to mark properties that didn’t apply to a clue.

I also used my favourite mathematical tool, WolframAlpha, to identify the following:

• tetrahedral numbers, n(n + 1)(n + 2)/6: 1, 4, 10, 20, 35, 56, etc
• Mersenne primes: 3, 7, 31, 127, 8191, etc
• Fermat primes: 3, 5, 17, 257, 65537, etc
• Perfect numbers: 6, 28, 496, 8128
• Numbers whose reverse is divisible by the number: 1089, 2178 and palindromes

Unfortunately, none of this prevented me from diving headlong towards dead-end number two, which was overlooking 901 as a possible entry for 34ac (reverse of a prime but not a prime).

Third time lucky, and my grid looked like this:

And I managed to successfully complete the puzzle like so:

Thanks for an excellent mathematical, Smudge.