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 the end of a on the sqrt(2) box, and put the stick b with ant y at the end of b on the sqrt(3) box, then make the two ants move simultaneously. 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 end 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 previous ends and start moving 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. Put the two ants in the end and the 2/3 position of a, make them move towards each other, and where they meet indicates 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 the end of a on the sqrt(2) box, and put the stick b with ant y at the end of b on the sqrt(3) box, then make the two ants move simultaneously. 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 end 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 previous ends and start moving 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. Put the two ants in the end and the 2/3 position of a, make them move towards each other, and where they meet indicates 1/3 meter.
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