Can't solve my own puzzle!
Can't solve my own puzzle!
Hi folks,
This a little embarrassing  I made a puzzle a few years ago, and I've lost the notebook that had the solution in. All I have is the puzzle itself, and I'm struggling to solve it. I would have checked it at the time that it had a unique solution that was logically reachable, but now I come to look at it I can place 16 numbers and then I'm stuck.
The rules are as follows:
Place the numbers 1 to 100 in the white squares of the grid so that:
Each number in a black square is the sum of the white squares bordering on it (horizontally and vertically, but not diagonally).
Each even number is on the same row or column as the preceding odd number.
Each odd number is on the same diagonal as the preceding even number. The second page is there so that you can cross of numbers as you use them, and also so that you can keep track of which pairs of numbers share a row/column (+), and which share a diagonal (x).
If anyone can work out the solution for me I would be very grateful.
Elliott
This a little embarrassing  I made a puzzle a few years ago, and I've lost the notebook that had the solution in. All I have is the puzzle itself, and I'm struggling to solve it. I would have checked it at the time that it had a unique solution that was logically reachable, but now I come to look at it I can place 16 numbers and then I'm stuck.
The rules are as follows:
Place the numbers 1 to 100 in the white squares of the grid so that:
Each number in a black square is the sum of the white squares bordering on it (horizontally and vertically, but not diagonally).
Each even number is on the same row or column as the preceding odd number.
Each odd number is on the same diagonal as the preceding even number. The second page is there so that you can cross of numbers as you use them, and also so that you can keep track of which pairs of numbers share a row/column (+), and which share a diagonal (x).
If anyone can work out the solution for me I would be very grateful.
Elliott

 Posts: 605
 Joined: Tue 29 Jun, 2010 11:41 am
Re: Can't solve my own puzzle!
Fairly stuck so far, probably at the same point you're at, but it strikes me that there might a toehold in the topright corner. I reckon 1/7/10/11/12/13 all place trivially elsewhere, leaving 6/14 accordingly unavailable, which leaves it pretty tightly constrained for finding a triple to fulfil the 23 clue. There must be a 15 or above in that triplet (985 isn't enough to meet the sum), which I think gives only 2318, 2417, 2516, 3416, 3515 as possibilities. Can we rule some of those out because they'd have to break the consecutive number placement rules?
Re: Can't solve my own puzzle!
Thanks Nick
I'm fairly sure there must be a mistake somewhere, as I keep meeting contradictions.
I placed trivially 1,34,12,7,10,63,33,48,13,100
I traced diagonal pair sums from the 102 at bottom right to place 49 above the 153 on left hand side.
Using the same method I traced from the 171 sum to place 70 below the 203 on the left hand side.
I placed 11 (from 10 and 12), and therefore 73, 35 and 62.
Now I tried to place 71 and 72, orthogonal to each other and diagonal to 70 and 73 respectively.
I worked out that either one or both had to be in the area around 204/242, I listed all possibilities and eliminated all but one, placing (from above the 203, clockwise) 55,38,72,23,71,67.
Then I turned my attention to the area you were looking at, and listed all the possibilities for the five squares in the top right, and eliminated every last one!
Either I made an unwarranted assumption in the placement of 71 & 72, or I made a typo when I copied it from my (now missing) notebook. I'm becoming more convinced it is the latter.
Sorry if I wasted people's time.
Elliott
I'm fairly sure there must be a mistake somewhere, as I keep meeting contradictions.
I placed trivially 1,34,12,7,10,63,33,48,13,100
I traced diagonal pair sums from the 102 at bottom right to place 49 above the 153 on left hand side.
Using the same method I traced from the 171 sum to place 70 below the 203 on the left hand side.
I placed 11 (from 10 and 12), and therefore 73, 35 and 62.
Now I tried to place 71 and 72, orthogonal to each other and diagonal to 70 and 73 respectively.
I worked out that either one or both had to be in the area around 204/242, I listed all possibilities and eliminated all but one, placing (from above the 203, clockwise) 55,38,72,23,71,67.
Then I turned my attention to the area you were looking at, and listed all the possibilities for the five squares in the top right, and eliminated every last one!
Either I made an unwarranted assumption in the placement of 71 & 72, or I made a typo when I copied it from my (now missing) notebook. I'm becoming more convinced it is the latter.
Sorry if I wasted people's time.
Elliott
Re: Can't solve my own puzzle!
Maxelkat,
There is no possibility of filling the upper right hand corner: The number left to the 42clue (which must be at least 21, because of Nicks reasoning) must have one neighboring number on its diagonal. But this diagonal is VERY short, namely 2 squares, both of which belong to the 23clue. There can't be a "20 or more" number there!
Thus the puzzle has no solution. Where you place the 71/72 does not matter.
Have fun, Stefan
There is no possibility of filling the upper right hand corner: The number left to the 42clue (which must be at least 21, because of Nicks reasoning) must have one neighboring number on its diagonal. But this diagonal is VERY short, namely 2 squares, both of which belong to the 23clue. There can't be a "20 or more" number there!
Thus the puzzle has no solution. Where you place the 71/72 does not matter.
Have fun, Stefan
Re: Can't solve my own puzzle!
Great insight Stefan,
so that means that the mistake (assuming there is only one mistake) must be with either the 42 or the 23, so maybe I can salvage the puzzle after all.
Thanks
Elliott
so that means that the mistake (assuming there is only one mistake) must be with either the 42 or the 23, so maybe I can salvage the puzzle after all.
Thanks
Elliott

 Posts: 605
 Joined: Tue 29 Jun, 2010 11:41 am
Re: Can't solve my own puzzle!
Haven't got a printout of the puzzle to hand to check it out properly, but all things considered the chances of 42 being a typo for 24 seem very high.
Re: Can't solve my own puzzle!
I have managed to get it to work by changing both the 42 and the 23 (to 32 and 83 respectively). I can be pretty sure that it was as the original puzzle, as the probability of everything else working otherwise is vanishingly small.
Here is the corrected puzzle: Sincere thanks to Nick and Stefan for your help
Elliott
Here is the corrected puzzle: Sincere thanks to Nick and Stefan for your help
Elliott