Question

Arrange these seven numbers and eight dots ( --> . )
.4.5.6.7.8.9.0.
so they add up to eighty two.

Answer 1

can you help with this?
@Calcmathlete @agentx5

Answer 2

Are the dots representing comma separated values (i.e. a sequence), decimal points, or \(\large \cdot\) for multiplication?

Answer 3

they can be any dot in math operations. decimals, multiplication, repeating numbers, anything else?

Answer 4

Oh... so we can choose the operand we want? :-3

I would recommend starting with the prime factorization of 82 in that case, can you do this step? :-)

Answer 5

82 = 2 x 41

Answer 6

Yep, and right away we can see that's only going to help us so far because 41 is prime. So now for the listing of addition/subtraction options using our "factors" from the list

8*9 = 72
7*9 = 63
etc...

We can see that won't be good either because brute force method here is going to be 823543 possible combos... Yeah no. Ok for computers, not good for neuron cells.

So getting creative...

I'm going to try to minimize each product, and because of symmetry they're all going to be even (which we'll need for 82):
4*9 = 36
5*8 = 40
6*7 = 42

Hmm so 5*8 + 6*7 = 82

But did we have to use all of these?

Answer 7

If so, it will get even more complicated because you'll be needing to use subtraction as well, or you will break 82 (think of a game of BlackJack, aka. 21, if you need a parallel as to why)

Answer 8

OK. I googled the question. It turns out that it is an old problem.
http://www.mathsisfun.com/puzzles/our-columbus-problem.html
I would've never gotten that!

Answer 9

Critical need-to-know information I was missing in the question:
"The dot over a number signifies that it is a repeater which would go on for ever"

>_<

Tough puzzle though!

Answer 10

nice try.