Fay’s Nines was a problem where you had to make the number 999 with the digits 1-9 (they can only be used once in every sum) and you had to use vertical addition…

To make the number, the units column had to make 19, the tens had to make 18 and the hundreds had to make 8. The reason for this is because you need to carry to the tens column and the hundreds column, therefore they had to be the number 8+1 form the units and tens to=9

At first i was just playing around with the numbers, trying to find answers. I would swap numbers with each other, for example if there was a 8 and 3 in the units and a 9 and 2 in the tens. I would change the 9 and 8 etc…

I discovered some rules and patterns during this task and here are the ones i found…

-the units column had to=19

-the tens column had to=18

-the units column had to=8

-the number ‘1’ cannot be in the units column

-each column can have 6 answers but rotating the three numbers around in the same column.

As i dug deeper into the problem i thought i would find all the possible units, tens and hundreds column solutions. This would break the problem into smaller parts and make it easier to find a pattern.

I got as far as finding all the possible solutions for the units and tens column and figuring out a system which involves rotating numbers around one of the digits in the center. I found 30 solutions for the units and 3o solutions for the tens. I didn’t exactly make it to the stage of trying out my little system but i had a good feeling about it. I planned to do the first 3 or so combinations in the center before i tried to find a pattern.

A lot of the time i would get stuck on finding a pattern and it was so frustrating. The second part of the problem with letters i found was basically the same and just made the problem a whole lot trickier so i continued on with what i started with. So the most difficult part was definitely was the combinations involving the letters.

Overall i enjoyed this problem a lot 🙂