Late Friday Puzzler -- simple(?) Addition

Re: Late Friday Puzzler -- simple(?) Addition

Larry Barrett

Assuming you meant 1,3,... instead of 1.3, ... here is the start of one solution:

(13+7) + (11-1) + ( - ) = 30.

Yes and No

Alex Y

You are correct that 1.2 was a typo, and it should have been 1,3.

But + and - are not in the list of things you can put in the parentheses.

Well shucks, and a question

Larry Barrett

I thought (13+7) + (11=1) + (9/3 - 15/5) = 30 was a pretty good solution.

Can commas appear in the answer?

Very good. More?

Alex Y

Good solution, given that I didn't specify that the parentheses could be filled ONLY from the list.

But there are other solutions that fill the solution only from the list.

Yes, you can use the commas.

Hint 1

Alex Y

One solution may come more naturally to those living in the areas colored green in this map:

Hint 2

Alex Y

Hint to another solution:

What if we had three hands?

Re: Hint 1

Larry Barrett

I think your hint suggests something like this:

(1,57) + (13,39) + (15,11)

This adds to 30.07, so I have not found the correct solution, but I think it will take this form.

On the right track

Alex Y

Unlike your numbers, though, you can just take a substring for each parenthesis.

Re: Hint 1 solution

Alex Y

Larry got VERY close on this one. The map showed countries where the divider between the units and tenths place of a number was "." (blue} or "," (green) If you were from one of the green countries, you might have looked at the list of numbers and come up with something like (7,9) + (13,1) + (9) = 30.

Re: Hint 2A

Alex Y

Okay, so you didn't like the three hands hint. What if humans had evolved with eleven fingers?

I did say that solutions to this one were outside the box, didn't I? ;-)

Re: Hint 2A

Henry Higginbotham

I did like the three-hands hint, if I took it correctly. I assumed you were suggesting base 15, and that now you're suggesting base 11. I tinkered with different bases when you first posted it, but that would have used only six of the eight numbers. Using some as decimals to make non-whole numbers didn't occur to me.

Correct! (and an apology)

Alex Y

Henry has the second solution I have seen.

Rereading the problem, I see where Henry thought he had to use all the numbers. I should have said to fill in the parentheses FROM rather than WITH the list. Sorry for the confusion.

There is a solution for any odd base from 11 - 19. For instance, that race of aliens with five fingers on each of their three hands would find

(13) + (15) + (7) = 30

to be true.

Re: Undeserved credit

Henry Higginbotham

I didn't really have a solution--just a hunch. Number bases are not a strong suit with me (or math in general, for that matter--I was an accounting major, for which a 4-function calculator sufficed in the early '70s). I can sometimes stumble through by empirical means and come up with a solution like 5 + 13 + 15 = 30 (base 13), but I can't get there in any sort of orderly manner.

Re: Undeserved credit

Alex Y

Nah, credit is given for the out-of-the-box thinking, not for the arithmetic. As far as doing the calc, what I realized is that is is a lot like doing it in base ten, except that you "carry" when the sum of a column get to the base. So for your example of 15+13+5 base 13, the rightmost digits 5+3+5 = 0, carry 1. The next column is 1+1 +(the carried)1 = 3.