Setting the Table

Since 13 is the smallest row, we’ll try that next: 13 = 6 + _ + _. Candidates are: 2 + 5, 3 – 4. Guess again:

The only possibility for row 3 is: 14 = 8 – 1 + 5, but this won’t work: if you put 5 in column 3 then: 11 = 5 + 3 + 3 and if you put 1 in column 3 you get: 11 = 1 + 3 + 7. Let’s swap the 3 and 4 in row two and see what happens:

Now we try column three: 11 = 5 + 4 + 2, which works and then column one: 13 = 1 + 3 + 9, which also works.

Fortunately, the row one sum works out and the puzzle is solved. Our choice and placing of 6 and 8 at the start was lucky indeed! Is there a better strategy .. try to find one.

Have fun!

Here is a 4x4 puzzle so we have the numbers 1 2 3 4 ... 14 15 16 to work with. Clearly we can put a 6 in row 4, column 2 since: 15 + 5 + 13 + 6 = 39

Luck is with us since we can put a 10 in row 4, column 1 since: 6 + 4 + 8 + 10 = 28.

Since column 1 needs only two more numbers, we give it a try. We need two numbers whose sum is 25, the allowed candidates are: 16 + 9 and 14 + 11. (The other possibilities: 15 + 10 and 13 + 12 use numbers that are already in the table.) We'll try 16 + 9:

More guessing: row 1 needs a pair that sums to 14, the allowed candidates are: 2 + 12 and 3 + 11. Let's try 3 – 11:

Lets work on row 3 (it has a large total which will limit possibilities). We need a pair that sums to 21. 7 + 14 is the only possibility.

So row 2, column 3 must be 9, which is already used so it is not allowed. Where did we go wrong? So many possibilities! The order the numbers are placed matters, maybe the 7 and 14 should be swapped?? After seeing this example, no will want to play this game unless they come up with a better strategy! Start with a 2x2 or 3x3 table, and see how that goes!

Have fun?