Nice idea, but if the sequel is in base-12 I’m going to scream

Welcome back to George vs the Listener Crossnumber!  Elap got us off to a rollicking start with the hailstone numbers in February, so let’s see what Oyler has in store.

Triples of squares that include all digits 1-9. I wonder how many of those there can be?  There’s only six possibilities for the two digit ones at least, and all of them appear to be in the grid.

There appears to be a nice juicy starting point – if J is one of the two digit primes and so is X, then we are looking for one that can be multiplied by 7 to get the starting digit of the other.  Combine that with K having to start with the second digit of 1 down and there is J = 16, X = 25 and K = 784 confirmed right off the bat!  L has to be some combination of 2,3,5,9 and the only one that is a square is 5329.  This might not be as difficult as it looks!

And it wasn’t… within an hour or so I had a complete grid and an inking of what should be going on – the bottom row was 847159236, which is 29106 squared and has all the digits 1-9.

Here’s the catch – I couldn’t find any other row or column that worked in that fashion, but there should be three of them! The final column is close – if the 2 I had in 35 across was a 9 then it would be the square of 20316.  Bugger!  Backtrack time!

Fortunately it didn’t take long to find, and my error only messed up a few key cells – I had put 798 for 27 across when it was 898.  This only changed five cells, but they were exactly the five cells I needed.  Woohoo!

My working grid for Listener 4399, Square Time Sums by Oyler

Oyler sent me an email during the week (and I’m sure there would have been some gloat factor if I had messed it up) so I think I can chalk this one up as a Victory to George!  He also mentioned that there is another hidden gem in here.  So well hidden that I have no clue. I guess I should go look over a Listen With Others to see what the professionals have to say.

2016 tally:  17-2-2

Feel free to tell me that it’s a square of something, and I’ll see you next week when Dysart brings us a puzzle that shows the number of steps to heaven is nine less than the number of steps to sobriety.  I’m fine down here.


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