Open Middle®
Directions: Using the digits 0 to 9, at most one time each, place a digit in each box to make an equivalent ratio with a unit rate that has greatest possible value.
Hint
How can you tell when two ratios are equivalent?
Answer
The greatest possible unit rate is 9 and can be made using a ratio like 9:1 = 27:3
Source: Robert Kaplinsky
9:1=27:3
26 equations fulfill the criteria:
3/1 = 24/8
3/1 = 27/9
4/1 = 20/5
4/1 = 28/7
4/1 = 32/8
4/1 = 36/9
5/1 = 20/4
5/1 = 30/6
5/1 = 40/8
6/1 = 30/5
6/1 = 42/7
6/1 = 54/9
7/1 = 28/4
7/1 = 42/6
7/1 = 56/8
7/1 = 63/9
8/1 = 24/3
8/1 = 32/4
8/1 = 40/5
8/1 = 56/7
8/1 = 72/9
9/1 = 27/3
9/1 = 36/4
9/1 = 54/6
9/1 = 63/7
9/1 = 72/8
Out of these, the one with the greatest possible value are the last 5: 9/1 = 27/3 = 36/4 = 54/6 = 63/7 = 72/8
Why use only 1 in a denominator? How about ratios such as 3/2 = 81/54?
i did 27 good job still