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4054: Leo’s Square Root of 576 (or If Only It Were That Easy)

Posted by Dave Hennings on 23 October 2009

This is the first puzzle from Leo that I’ve done, although I see he has had four previous Listeners back in the late 90’s and 2002. Not knowing the level of difficulty made me tackle this fairly soon after publication so that I could devote as much time as possible to any final step difficulty. As well as the almost obligatory extra letters in the wordplay of most clues, the preamble offered us “extra material” (but only in some clues), “information that should prove helpful”, and a requirement to finally “adjust the initial grid”.
1 across seemed as good a place as any to start, and I was more than happy to find that POST HASTE, CHANTEUR and REALM in the top right corner came fairly quickly, as did my checking of Chambers to see that it contained ‘chanteur’, which I guessed was French for singer. Lucky for me that I did, as it wasn’t there, but CHAUNTER was, although 7dn beginning HN… would have probably prevented too much wasted time.
5dn and 8dn were easy clues, except that they were 3-letter answers, SHA and ANT which were allotted four squares. Each of these clues had a superfluous word (extra material) in “apostles” and “crew”. 12 for the apostles and probably 8 for the crew, and it seemed that the empty squares were to be given numbers … a very early discovery compared to many recent puzzles which have had me guessing way past completion of the actual grid.
Clue-solving progressed, with TALOOKA, HUMPH, TETANAL in the top right and then AVARICE, LUGANO, STEEL DRUM and RAGBAGS in the bottom right. In fact, unusually, I pretty much solved each corner of this puzzle in sequence, finishing with bottom left and then top left corners. The clues were on the easy side for a Listener, and the extra material was not too difficult to find and resolve. The nine numbers resulted in a magic square adding to 45, which is not the square root of 576:
l4054-square-1
It was fairly obvious that the grid had to be completed with letters substituted for the numbers and giving a “totally satisfying” grid complete with real words. The trouble was that TWENTY-ONE, TWENTY-TWO, THIRTY-ONE and THIRTY-TWO all resulted in real words, so the next question was how to decide between the four.
Well, the extra letters in the clues without thematic material gave LETTER COUNT GIVES A SECOND MAGIC SQUARE. So, assigning their sequential alphabetical number to each of the letters would somehow resolve the dilemma. About forty minutes of running around in circles, “adding up” either the letters surrounding the numerical squares or some other such futile groups of letters obviously resulted in nothing. I think it was reading the extra letters phrase for the umpteenth time that finally put me on the right track … it was the number of letters in the numbers spelt out as words that was the clue: 25 has 10 letters, 8 has 5 and 12 has 6, etc. It was such a relief as I worked my way through the nine numbers and found that each had a different number of letters:
L4054 Square 2
This magic square adds up to 21, so TWENTY-ONE is used to “literally adjust the grid” to make it totally satisfying. A final confirmation is that the first magic number (45) minus the second (21) gives 24, the square root of 576. Not a difficult puzzle from Leo, but really enjoyable nonetheless.

2 Responses to “4054: Leo’s Square Root of 576 (or If Only It Were That Easy)”

  1. erwinch said

    I would say that it was more than fairly obvious that only letters were to appear in the final grid.  There has to be a point to it all and just planting a magic square into the centre of a word grid with entries such as ta11ra and le9d is totally meaningless.  In the past we have seen numbers replace letters so that we could have fr8er crossing heavyw8, for example, but some numbers are much easier to accommodate in this way than others.  Leo might have considered this approach but I personally think it a hackneyed device now.

    As you may have gathered from my blog below, I am not exactly overwhelmed by the ‘magic’ quality of these squares and reading about them on the Net we find that there are an infinite number of alphamagic squares.  We can quickly generate trivial examples by adding constants that do not alter the digits of our existing square.  For example, adding 4200 to each digit adds four thousand two hundred and or 25 letters to each digit in our second square, maintaining the magic.  I have looked on the Net but have yet to see a non-trivial English example other than the one that Leo used.  I wonder if there are any others using only numbers under one hundred?  We might extend the range by adding a few negative numbers to add the five letters in minus to the second square and zero might be alternatively nought or nil.  Of course, none of this detracts from Leo’s splendid puzzle.

  2. Erwin
    I agree that blatantly obvious would have better described my (albeit subjective) view that real words would appear in the final grid! However, a number of solvers have confessed to actually or nearly submitting a grid with the numbers of the second magic square in place, so I think my tactfulness paid off!
    Dave.

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