Open Middle®
Directions: Using the digits 1 to 9 at most one time each, fill in the boxes so that the sum is as close to 1/2 as possible.
Hint
How do you add fractions?
What kinds of fractions would you use to get close to 1/2?
What kinds of fractions would you use to get close to 1/2?
Answer
A possible solution is 2/8 + 1/4
Source: Daniel Luevanos
We think 3/9 + 1/6 also works!
Another possible solution is 3/9 + 1/6
I think that, together with the one that appears above, are the only two possible solutions.
I also agree with that.
The problem gets more and more interesting if you allow to use more than one digit in each box, or if you FORCE to use all nine digits, distributed as you like along the boxes (for example 48/97 + 6/1235, which approximates 1/2 with an error < 3×10⁻⁴).
Is it possible to get an exact 1/2?
What about 2/4 + 1/987653 ? (error < 1.02×10⁻⁶). Can you improve it?
I can confirm that 1/4 + 2/8 and 1/6 + 3/9 are the only valid expression that result in exactly 1/2.