Open Middle®
Directions: Using the digits 1 through 9, at most one each time, fill in the boxes to make the statement true.
Hint
Which denominators can be ruled out?
Answer
Multiple correct answers, e.g.
1/2 + 46/5 = 9.7
4/5 + 17/2 = 9.3
1/2 + 46/5 = 9.7
4/5 + 17/2 = 9.3
Source: Giselle Garcia
140 solutions:
14/7 + 3/6 = 2.5
18/9 + 3/6 = 2.5
14/7 + 3/5 = 2.6
18/9 + 3/5 = 2.6
14/7 + 6/5 = 3.2
18/9 + 6/5 = 3.2
12/6 + 7/5 = 3.4
16/8 + 7/5 = 3.4
18/6 + 2/5 = 3.4
18/9 + 7/5 = 3.4
14/7 + 9/6 = 3.5
18/6 + 2/4 = 3.5
18/9 + 6/4 = 3.5
21/7 + 4/8 = 3.5
21/9 + 7/6 = 3.5
26/8 + 1/4 = 3.5
27/9 + 4/8 = 3.5
14/7 + 8/5 = 3.6
16/5 + 2/4 = 3.7
16/5 + 4/8 = 3.7
12/6 + 9/5 = 3.8
14/7 + 9/5 = 3.8
21/7 + 4/5 = 3.8
27/9 + 4/5 = 3.8
12/5 + 6/4 = 3.9
17/5 + 2/4 = 3.9
17/5 + 4/8 = 3.9
36/9 + 1/5 = 4.2
12/8 + 9/3 = 4.5
18/6 + 3/2 = 4.5
21/7 + 9/6 = 4.5
28/7 + 3/6 = 4.5
36/9 + 1/2 = 4.5
21/7 + 8/5 = 4.6
27/9 + 8/5 = 4.6
28/7 + 3/5 = 4.6
16/5 + 3/2 = 4.7
21/5 + 3/6 = 4.7
36/8 + 1/5 = 4.7
21/7 + 9/5 = 4.8
17/5 + 3/2 = 4.9
21/6 + 7/5 = 4.9
36/8 + 2/5 = 4.9
14/5 + 7/2 = 6.3
18/4 + 9/5 = 6.3
29/5 + 4/8 = 6.3
17/5 + 9/3 = 6.4
18/3 + 2/5 = 6.4
14/7 + 9/2 = 6.5
18/3 + 2/4 = 6.5
31/5 + 2/4 = 6.7
31/5 + 4/8 = 6.7
32/5 + 4/8 = 6.9
26/4 + 3/5 = 7.1
28/5 + 6/4 = 7.1
28/5 + 9/6 = 7.1
18/3 + 6/5 = 7.2
63/9 + 1/5 = 7.2
14/5 + 9/2 = 7.3
29/5 + 6/4 = 7.3
63/9 + 2/5 = 7.4
14/2 + 3/6 = 7.5
18/3 + 6/4 = 7.5
18/3 + 9/6 = 7.5
18/4 + 6/2 = 7.5
18/4 + 9/3 = 7.5
18/6 + 9/2 = 7.5
21/3 + 4/8 = 7.5
28/4 + 3/6 = 7.5
29/6 + 8/3 = 7.5
41/6 + 2/3 = 7.5
63/9 + 1/2 = 7.5
63/9 + 2/4 = 7.5
63/9 + 4/8 = 7.5
14/2 + 3/5 = 7.6
28/4 + 3/5 = 7.6
21/3 + 4/5 = 7.8
24/5 + 3/1 = 7.8
24/5 + 9/3 = 7.8
29/5 + 6/3 = 7.8
63/9 + 4/5 = 7.8
32/5 + 6/4 = 7.9
49/7 + 6/5 = 8.2
26/4 + 9/5 = 8.3
21/3 + 7/5 = 8.4
27/5 + 3/1 = 8.4
27/5 + 9/3 = 8.4
63/9 + 7/5 = 8.4
14/2 + 9/6 = 8.5
16/4 + 9/2 = 8.5
21/3 + 6/4 = 8.5
21/3 + 9/6 = 8.5
27/6 + 4/1 = 8.5
39/6 + 2/1 = 8.5
39/6 + 4/2 = 8.5
47/6 + 2/3 = 8.5
49/6 + 1/3 = 8.5
49/7 + 3/2 = 8.5
72/9 + 3/6 = 8.5
23/5 + 4/1 = 8.6
72/9 + 3/5 = 8.6
41/5 + 3/6 = 8.7
37/5 + 6/4 = 8.9
42/5 + 3/6 = 8.9
38/5 + 6/4 = 9.1
36/4 + 1/5 = 9.2
36/5 + 8/4 = 9.2
63/7 + 1/5 = 9.2
17/2 + 4/5 = 9.3
16/2 + 7/5 = 9.4
37/5 + 2/1 = 9.4
63/7 + 2/5 = 9.4
18/2 + 3/6 = 9.5
18/3 + 7/2 = 9.5
26/4 + 3/1 = 9.5
27/3 + 4/8 = 9.5
28/3 + 1/6 = 9.5
36/4 + 1/2 = 9.5
37/4 + 2/8 = 9.5
41/6 + 8/3 = 9.5
48/6 + 3/2 = 9.5
62/8 + 7/4 = 9.5
63/7 + 1/2 = 9.5
63/7 + 2/4 = 9.5
63/7 + 4/8 = 9.5
64/8 + 3/2 = 9.5
72/8 + 3/6 = 9.5
18/2 + 3/5 = 9.6
24/3 + 8/5 = 9.6
28/5 + 4/1 = 9.6
32/4 + 8/5 = 9.6
38/5 + 2/1 = 9.6
38/5 + 4/2 = 9.6
72/8 + 3/5 = 9.6
38/4 + 1/5 = 9.7
41/5 + 3/2 = 9.7
46/5 + 1/2 = 9.7
27/3 + 4/5 = 9.8
34/5 + 6/2 = 9.8
63/7 + 4/5 = 9.8