And the answer is?

Steven G

Elite Member
Joined
Dec 30, 2014
Messages
14,364
Using all the numbers 1-18 can you fill in the 18 blanks?

_ + _ = _

_ + _ = _

_ + _ = _

_ + _ = _

_ + _ = _

_ + _ = _
 
I think it can't be done. The sum of all numbers is 171. Needs to be even to get equal sums on the left and right sides.
 
Looks like Sir Jomo zatryin' to pull a fast one...
:D Did your computer show you this or do you have a proof, actually a very simple proof?

I did use the word can and a question mark in my post!
 
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1 + 11 = 12

4 + 14 = 18

13 + 2 = 15

8 + 3 = 7

6 + 10 = 16

9 + 5 = 17

-----

There, I did it. Technically, no one ever said the equations had to be correct, just that I had to fill in the blanks. ;)
 
1 + 11 = 12

4 + 14 = 18

13 + 2 = 15

8 + 3 = 7

6 + 10 = 16

9 + 5 = 17

-----

There, I did it. Technically, no one ever said the equations had to be correct, just that I had to fill in the blanks. ;)
i don't know about that!
 
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Using all the numbers 1-12 can you fill in the 12 blanks?

_ + _ = _

_ + _ = _

_ + _ = _

_ + _ = _

That one has 6 solutions.

Find them...then I'll answer your question :cool:
OK tough guy, here is the solution. 1st the total sum of the 12 numbers is 78. 12, being the largest number, must be on the rhs. The rhs must sum to 39 = 78/2 which can only happen if the rhs is 12,11,10, 6 or 12,11,9, 7 or 12,10, 9, 8

The 7 answers are (you even get a bonus 1! = 1) :
3+9=12
4+7=11
8+2=10
1+5=6

10+2=12
8+3=11
5+4=9
6+1=7

10+2=12
5+6=11
1+8=9
3+4=7

4+8=12
2+9=11
3+7=10
1+5=6

8+4=12
10+1=11
6+3=9
2+5=7

1+11=12
3+7=10
4+5=9
6+2=8

1+11=12
4+6=10
2+7=9
3+5=8

The problem is that I gave away the proof to my original question!
 
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The 8 answers are (you too get a bonus of 1!):
the 7 you showed
and:
1 + 9 = 10
2 + 4 = 6
3 + 8 = 11
5 + 7 = 12

"The problem is that I gave away the proof to my original question!"
Too bad, so sad :lol:

Oh by the way, the 2 I missed were on purpose: to make you feel better :lol:
How did I miss that one. There was NEVER any doubt in my mind, even before I found more than 6, that there would be more than 6 solutions. I know you better than that.

I'd still like to see your proof. It could be slightly/very different than mine.
 
Using all the numbers 1-12 can you fill in the 12 blanks?

_ + _ = _

_ + _ = _

_ + _ = _

_ + _ = _

That one has 6 solutions.

Find them...then I'll answer your question :cool:
Find them...then I'll answer your question
 
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