# My colleague gave me a number puzzle

My colleague probably has left work now, he is no longer responding. He gave me this puzzle and asked me to fill in the '?':

4 | 5 | 8 | 3 | 7
6 | 3 | 7 | 5 | 6
8 | 2 | 3 | 7 | 9
2 | 3 | 5 | 1 | 8
1 | 9 | 2 | 1 | 7
9 | 4 | 6 | 8 | ?


I tried seeing patterns from different angles. After a while I asked for a clue:

Him: It's a mathematical puzzle
Me: Are you supposed to insert operators(-+*/)
Him: Yes
Him: I can tell you it is a Mensa creation

I don't have the answer for this puzzle. But I suspect I'll get it next week if you don't get there first! I am out of ideas

• Let's see, it's not quite an N✖N matrix, neither is it sudoku-style, neither can it realistically be a system of equations (the last number could be anything). Perhaps each line (after you fill in operations) amounts to the same number?
– NH.
Oct 20 '17 at 15:16

Perhaps involving only subtracting,

the number formed by joining the numbers in last two columns is obtained by subtracting the number in the 3rd column from the number formed by joining numbers of first two columns...going by this, it should be 94 - 6= 88 and hence 8 is the answer.

For example,

| 1 | 9 | - | 2 | = | 1 | 7 |and so on...

• I like this! Youll get the tick on monday if it proves correct!
Oct 20 '17 at 17:45
• @Adam If this didn't turn out to be the correct solution, the puzzle would be a really bad one. On the other hand it could be easily turned into an awesome one just by saying "There are 2 different solutions, and they both make sense". But I bet this is the only solution. Oct 21 '17 at 0:40

One solution is that

a + b = c + d + e (mod 9)

It doesn't necessarily fit the hint, depending on your view on the last bit. But it does work, and gives you a value of

8

for the ?.

• This is probably somewhat equivalent to Mea Culpa Nay’s answer. But, it doesn't quite work in all instances because 0=9 (mod 9) which means that if the question mark were in the last position of line 3 (for example) you wouldn't get an unambiguous solution. Oct 20 '17 at 22:31
• @DrXorile It could be noted that all numbers are digits 1-9 (excluding 0). Also if you look at the timestamp, this came before Mea's answer so it couldn't've been a copy Oct 21 '17 at 2:48
• I saw the timestamp. I certainly wasn't accusing you of anything! Sorry if that came across. I was just arguing that mod 9 would result in a number ≤8, which didn't quite fit. It's an excellent start and I gave you a +1. Oct 22 '17 at 0:28