A Gaping Hole
Am I?Posted: Wed Apr 5 2017 12:56 pm

I alone can't fill. 


The nice fishPosted: Mon Apr 10 2017 06:29 am

Here's one solution, but it's a bit tedious. There are probably better solutions, and even guessing would probably be quicker.

This blue square, http://imgur.com/yOTMgzV, must be between 2 and 5, since the vertical 34 column already have three squares that's 6 or higher.

Then, adding these rows, http://imgur.com/dpuJMjx, and subtracting these columns, http://imgur.com/vO2daKG, we find that the sum of these three squares, http://imgur.com/sL89Feq, must be 15. Therefor, the bottom square can't be 4 or 5, since that would leave the top left to be 6, which would not be possible.

Now, to maintain the sum of 15, if the top left is 9, the other two must be 2+4. However, this is not possible since this blue square, http://imgur.com/AeFFyJp, should be 2 or 4. Therefor, the top left is 7, and we get can solve from here on, http://imgur.com/580kEiD

Last Edited: Mon Apr 10 2017 06:31 am
Am I?Posted: Mon Apr 10 2017 10:00 am

Oh, wow. That's ingenious. Thank you so much :)