Open Middle®
Directions: Using the digits 1 to 9 at most one time each, place a digit in each box to make a true equation with the smallest possible sum.
Hint
Which digits should you use/avoid? Where should you put the 1? The 2? The…
Answer
The best answer found so far is 1 5/8 + 2 6/8 = 4 3/8.
Source: Robert Kaplinsky
9 1/8 + 2 2/8 = 11 3/8
6 1/8 + 6 3/8=12 4/8
What about 1 4/8 +2 5/8 = 3 9/8?
1 5/8 + 2 6/8 = 4 3/8.
Without any further restrictions, there are 188 solutions (plus another 188 where the addends are swapped). If the mixed numbers can’t have an improper fraction as the fractional part, there are 94 solutions left:
1 5/8 + 2 6/8 = 4 3/8
1 6/8 + 2 5/8 = 4 3/8
1 6/8 + 2 7/8 = 4 5/8
1 7/8 + 2 6/8 = 4 5/8
1 2/8 + 3 5/8 = 4 7/8
1 5/8 + 3 2/8 = 4 7/8
1 4/8 + 3 6/8 = 5 2/8
1 6/8 + 3 4/8 = 5 2/8
2 1/8 + 3 6/8 = 5 7/8
2 6/8 + 3 1/8 = 5 7/8
2 4/8 + 3 5/8 = 6 1/8
2 5/8 + 3 4/8 = 6 1/8
1 3/8 + 4 7/8 = 6 2/8
1 7/8 + 4 3/8 = 6 2/8
2 5/8 + 3 7/8 = 6 4/8
2 7/8 + 3 5/8 = 6 4/8
1 3/8 + 5 4/8 = 6 7/8
1 4/8 + 5 3/8 = 6 7/8
2 3/8 + 4 6/8 = 7 1/8
2 6/8 + 4 3/8 = 7 1/8
1 4/8 + 5 6/8 = 7 2/8
1 6/8 + 5 4/8 = 7 2/8
2 5/8 + 4 6/8 = 7 3/8
2 6/8 + 4 5/8 = 7 3/8
2 1/8 + 5 3/8 = 7 4/8
2 3/8 + 5 1/8 = 7 4/8
1 2/8 + 6 3/8 = 7 5/8
1 3/8 + 6 2/8 = 7 5/8
3 1/8 + 4 5/8 = 7 6/8
3 5/8 + 4 1/8 = 7 6/8
2 3/8 + 5 6/8 = 8 1/8
2 6/8 + 5 3/8 = 8 1/8
3 2/8 + 4 7/8 = 8 1/8
3 7/8 + 4 2/8 = 8 1/8
1 3/8 + 6 7/8 = 8 2/8
1 7/8 + 6 3/8 = 8 2/8
1 4/8 + 6 7/8 = 8 3/8
1 7/8 + 6 4/8 = 8 3/8
2 4/8 + 5 7/8 = 8 3/8
2 7/8 + 5 4/8 = 8 3/8
1 5/8 + 6 7/8 = 8 4/8
1 7/8 + 6 5/8 = 8 4/8
2 1/8 + 6 3/8 = 8 4/8
2 3/8 + 6 1/8 = 8 4/8
1 2/8 + 7 3/8 = 8 5/8
1 3/8 + 7 2/8 = 8 5/8
2 1/8 + 6 4/8 = 8 5/8
2 4/8 + 6 1/8 = 8 5/8
3 6/8 + 4 7/8 = 8 5/8
3 7/8 + 4 6/8 = 8 5/8
1 2/8 + 7 4/8 = 8 6/8
1 4/8 + 7 2/8 = 8 6/8
3 2/8 + 5 4/8 = 8 6/8
3 4/8 + 5 2/8 = 8 6/8
2 3/8 + 6 4/8 = 8 7/8
2 4/8 + 6 3/8 = 8 7/8
3 1/8 + 5 6/8 = 8 7/8
3 6/8 + 5 1/8 = 8 7/8
2 4/8 + 6 5/8 = 9 1/8
2 5/8 + 6 4/8 = 9 1/8
3 2/8 + 5 7/8 = 9 1/8
3 7/8 + 5 2/8 = 9 1/8
1 4/8 + 7 6/8 = 9 2/8
1 6/8 + 7 4/8 = 9 2/8
3 4/8 + 5 6/8 = 9 2/8
3 6/8 + 5 4/8 = 9 2/8
1 5/8 + 7 6/8 = 9 3/8
1 6/8 + 7 5/8 = 9 3/8
2 4/8 + 6 7/8 = 9 3/8
2 7/8 + 6 4/8 = 9 3/8
4 1/8 + 5 2/8 = 9 3/8
4 2/8 + 5 1/8 = 9 3/8
2 1/8 + 7 3/8 = 9 4/8
2 3/8 + 7 1/8 = 9 4/8
2 5/8 + 6 7/8 = 9 4/8
2 7/8 + 6 5/8 = 9 4/8
1 2/8 + 8 3/8 = 9 5/8
1 3/8 + 8 2/8 = 9 5/8
2 1/8 + 7 4/8 = 9 5/8
2 4/8 + 7 1/8 = 9 5/8
3 1/8 + 6 4/8 = 9 5/8
3 4/8 + 6 1/8 = 9 5/8
1 2/8 + 8 4/8 = 9 6/8
1 4/8 + 8 2/8 = 9 6/8
2 1/8 + 7 5/8 = 9 6/8
2 5/8 + 7 1/8 = 9 6/8
1 2/8 + 8 5/8 = 9 7/8
1 3/8 + 8 4/8 = 9 7/8
1 4/8 + 8 3/8 = 9 7/8
1 5/8 + 8 2/8 = 9 7/8
3 2/8 + 6 5/8 = 9 7/8
3 5/8 + 6 2/8 = 9 7/8
4 1/8 + 5 6/8 = 9 7/8
4 6/8 + 5 1/8 = 9 7/8
There are no solutions with only fractions in their simplest form (because the numerators would all have to be uneven, but the sum of two uneven numbers is always even)
Assuming the whole number part of the mixed numbers is a one-digit number.
The smallest possible sum is therefore 4 3/8.
1 5/8 plus 6 7/8 equals 8 4/8
Without any further restrictions, there are 188 solutions (plus another 188 where the addends are swapped). If the mixed numbers can’t have an improper fraction as the fractional part, there are 94 solutions left:
1 5/8 + 2 6/8 = 4 3/8
1 6/8 + 2 5/8 = 4 3/8
1 6/8 + 2 7/8 = 4 5/8
1 7/8 + 2 6/8 = 4 5/8
1 2/8 + 3 5/8 = 4 7/8
1 5/8 + 3 2/8 = 4 7/8
1 4/8 + 3 6/8 = 5 2/8
1 6/8 + 3 4/8 = 5 2/8
2 1/8 + 3 6/8 = 5 7/8
2 6/8 + 3 1/8 = 5 7/8
2 4/8 + 3 5/8 = 6 1/8
2 5/8 + 3 4/8 = 6 1/8
1 3/8 + 4 7/8 = 6 2/8
1 7/8 + 4 3/8 = 6 2/8
2 5/8 + 3 7/8 = 6 4/8
2 7/8 + 3 5/8 = 6 4/8
1 3/8 + 5 4/8 = 6 7/8
1 4/8 + 5 3/8 = 6 7/8
2 3/8 + 4 6/8 = 7 1/8
2 6/8 + 4 3/8 = 7 1/8
1 4/8 + 5 6/8 = 7 2/8
1 6/8 + 5 4/8 = 7 2/8
2 5/8 + 4 6/8 = 7 3/8
2 6/8 + 4 5/8 = 7 3/8
2 1/8 + 5 3/8 = 7 4/8
2 3/8 + 5 1/8 = 7 4/8
1 2/8 + 6 3/8 = 7 5/8
1 3/8 + 6 2/8 = 7 5/8
3 1/8 + 4 5/8 = 7 6/8
3 5/8 + 4 1/8 = 7 6/8
2 3/8 + 5 6/8 = 8 1/8
2 6/8 + 5 3/8 = 8 1/8
3 2/8 + 4 7/8 = 8 1/8
3 7/8 + 4 2/8 = 8 1/8
1 3/8 + 6 7/8 = 8 2/8
1 7/8 + 6 3/8 = 8 2/8
1 4/8 + 6 7/8 = 8 3/8
1 7/8 + 6 4/8 = 8 3/8
2 4/8 + 5 7/8 = 8 3/8
2 7/8 + 5 4/8 = 8 3/8
1 5/8 + 6 7/8 = 8 4/8
1 7/8 + 6 5/8 = 8 4/8
2 1/8 + 6 3/8 = 8 4/8
2 3/8 + 6 1/8 = 8 4/8
1 2/8 + 7 3/8 = 8 5/8
1 3/8 + 7 2/8 = 8 5/8
2 1/8 + 6 4/8 = 8 5/8
2 4/8 + 6 1/8 = 8 5/8
3 6/8 + 4 7/8 = 8 5/8
3 7/8 + 4 6/8 = 8 5/8
1 2/8 + 7 4/8 = 8 6/8
1 4/8 + 7 2/8 = 8 6/8
3 2/8 + 5 4/8 = 8 6/8
3 4/8 + 5 2/8 = 8 6/8
2 3/8 + 6 4/8 = 8 7/8
2 4/8 + 6 3/8 = 8 7/8
3 1/8 + 5 6/8 = 8 7/8
3 6/8 + 5 1/8 = 8 7/8
2 4/8 + 6 5/8 = 9 1/8
2 5/8 + 6 4/8 = 9 1/8
3 2/8 + 5 7/8 = 9 1/8
3 7/8 + 5 2/8 = 9 1/8
1 4/8 + 7 6/8 = 9 2/8
1 6/8 + 7 4/8 = 9 2/8
3 4/8 + 5 6/8 = 9 2/8
3 6/8 + 5 4/8 = 9 2/8
1 5/8 + 7 6/8 = 9 3/8
1 6/8 + 7 5/8 = 9 3/8
2 4/8 + 6 7/8 = 9 3/8
2 7/8 + 6 4/8 = 9 3/8
4 1/8 + 5 2/8 = 9 3/8
4 2/8 + 5 1/8 = 9 3/8
2 1/8 + 7 3/8 = 9 4/8
2 3/8 + 7 1/8 = 9 4/8
2 5/8 + 6 7/8 = 9 4/8
2 7/8 + 6 5/8 = 9 4/8
1 2/8 + 8 3/8 = 9 5/8
1 3/8 + 8 2/8 = 9 5/8
2 1/8 + 7 4/8 = 9 5/8
2 4/8 + 7 1/8 = 9 5/8
3 1/8 + 6 4/8 = 9 5/8
3 4/8 + 6 1/8 = 9 5/8
1 2/8 + 8 4/8 = 9 6/8
1 4/8 + 8 2/8 = 9 6/8
2 1/8 + 7 5/8 = 9 6/8
2 5/8 + 7 1/8 = 9 6/8
1 2/8 + 8 5/8 = 9 7/8
1 3/8 + 8 4/8 = 9 7/8
1 4/8 + 8 3/8 = 9 7/8
1 5/8 + 8 2/8 = 9 7/8
3 2/8 + 6 5/8 = 9 7/8
3 5/8 + 6 2/8 = 9 7/8
4 1/8 + 5 6/8 = 9 7/8
4 6/8 + 5 1/8 = 9 7/8
There are no solutions with only fractions in their simplest form (because the numerators would all have to be uneven, but the sum of two uneven numbers is always even)
I think the least possible sum is 1 5/8 + 2 3/8 = 4
wrong!!
We were doing the least possible sum? Oh yeah.
the answer is 1/8+2/8 =3/8
You have to fill in the wholes field to answer correctly.
You CHEATED!!
I think its 1 5/8 + 2 6/8 = 4 3/8. 🙂
You copied the answer!
what no I didn’t!! >:(
1 5/8 + 2 6/8 = 4 3/8 that is the least one you can do
Ehhh.
1 2/8 + 3 5/8 = 4 7/8.
i dont know
dont know
(I like CHEESE!!)
I like Cheese too!!
i hate you🤬
YOU ARE MEAN!!!!!!!!! 😢😢😡😡😡🤬🤬👿👿
I don’t think you should be saying that as this is a public website, and your comment and name are never deleted.
I think that the amount of answer combinations go into hundreds, therefore there are many options
its 4 3/8