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The solution to get 1/3 meter.
Label the two sticks as a and b and the ants as x and y. Put the stick a with ant x at an its endpoint into the "sqrt(2)" box, and put the stick b with the ant y at its end in the "sqrt(3)" box. Make the two ants move simultaneously towards the other endpoint of the sticks. When the ant y get to the other end of the stick b, stop the ant x and mark its position at the stick a. The distance between the position and the starting endpoint of a should be sqrt(2)/sqrt(3)=sqrt(6)/3 meter. Mark the same position on the stick b, and put the two ants on the starting endpoints and make them move again. Stop the ant a when b get to the marked position, and then the ant x is at a new position which indicates (sqrt(6)/3) * (sqrt(6)/3) = 2/3 meter of the stick a, and certainly the distance of this position to the other endpoint is 1/3 meter.
The solution to get 1/3 meter.
Label the two sticks as a and b and the ants as x and y. Put the stick a with ant x at an its endpoint into the "sqrt(2)" box, and put the stick b with the ant y at its end in the "sqrt(3)" box. Make the two ants move simultaneously towards the other endpoint of the sticks. When the ant y get to the other end of the stick b, stop the ant x and mark its position at the stick a. The distance between the position and the starting endpoint of a should be sqrt(2)/sqrt(3)=sqrt(6)/3 meter. Mark the same position on the stick b, and put the two ants on the starting endpoints and make them move again. Stop the ant a when b get to the marked position, and then the ant x is at a new position which indicates (sqrt(6)/3) * (sqrt(6)/3) = 2/3 meter of the stick a, and certainly the distance of this position to the other endpoint is 1/3 meter.
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