Open Middle®
Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to make the equation true.
Hint
Where do you find it most manageable to begin placing digits?
Think about what digit will end up in the hundredths place of the difference based on the digit you use in the hundredths place of the subtrahend.
Think about what digit will end up in the hundredths place of the difference based on the digit you use in the hundredths place of the subtrahend.
Answer
There are multiple solutions. Three examples are:
1. 9.5 – 7.34 = 2.16
2. 8.7 – 3.29 = 5.41
3. 9.1 – 5.24 = 3.86
1. 9.5 – 7.34 = 2.16
2. 8.7 – 3.29 = 5.41
3. 9.1 – 5.24 = 3.86
Source: Adina Rochkind
18,27, 36,45…
9.8-4.63=5.17
5.90 – 3.74 = 2.16
666 + 666 = you will be dead
9.80 – 5.67 = 4.13
9.0-2.50=6.50
8.9 – 7.56 = 1.34
9.4-6.83=2.57
7.8-3.29 = 4.51
9.92-4.81=5.11
9.8 – 5.63 + 4.17
8.7 – 5.29 = 3.41
9.8 – 5.67 = 4.13
9.1 – 5.24 = 3.86
5.9 – 4.27 = 1.63
8.7 – 3.21 = 5.49
8.7 – 3.21 = 5.49
8.9 – 7.56 = 1.34
9.8 – 5.67 = 4.13
5.9 – 1.23 = 4.67
9.7 – 6.12 = 3. 58
8.6 – 3.49 = 5.21
5.4 – 3.78 = 1.62
5.9 – 4.67 = 1.23
7.8 – 2.31 = 5.49
9.5 – 2.36 = 7.14
5.9 – 4.23 = 1.67
208 solutions:
4.5 – 1.63 = 2.87
4.5 – 1.67 = 2.83
4.5 – 1.83 = 2.67
4.5 – 1.87 = 2.63
4.5 – 2.63 = 1.87
4.5 – 2.67 = 1.83
4.5 – 2.83 = 1.67
4.5 – 2.87 = 1.63
5.4 – 1.62 = 3.78
5.4 – 1.68 = 3.72
5.4 – 1.72 = 3.68
5.4 – 1.78 = 3.62
5.4 – 3.62 = 1.78
5.4 – 3.68 = 1.72
5.4 – 3.72 = 1.68
5.4 – 3.78 = 1.62
5.9 – 1.23 = 4.67
5.9 – 1.27 = 4.63
5.9 – 1.63 = 4.27
5.9 – 1.67 = 4.23
5.9 – 2.14 = 3.76
5.9 – 2.16 = 3.74
5.9 – 2.74 = 3.16
5.9 – 2.76 = 3.14
5.9 – 3.14 = 2.76
5.9 – 3.16 = 2.74
5.9 – 3.74 = 2.16
5.9 – 3.76 = 2.14
5.9 – 4.23 = 1.67
5.9 – 4.27 = 1.63
5.9 – 4.63 = 1.27
5.9 – 4.67 = 1.23
6.3 – 1.52 = 4.78
6.3 – 1.58 = 4.72
6.3 – 1.72 = 4.58
6.3 – 1.78 = 4.52
6.3 – 4.52 = 1.78
6.3 – 4.58 = 1.72
6.3 – 4.72 = 1.58
6.3 – 4.78 = 1.52
6.4 – 2.51 = 3.89
6.4 – 2.59 = 3.81
6.4 – 2.81 = 3.59
6.4 – 2.89 = 3.51
6.4 – 3.51 = 2.89
6.4 – 3.59 = 2.81
6.4 – 3.81 = 2.59
6.4 – 3.89 = 2.51
7.2 – 1.34 = 5.86
7.2 – 1.36 = 5.84
7.2 – 1.84 = 5.36
7.2 – 1.86 = 5.34
7.2 – 5.34 = 1.86
7.2 – 5.36 = 1.84
7.2 – 5.84 = 1.36
7.2 – 5.86 = 1.34
7.5 – 2.61 = 4.89
7.5 – 2.69 = 4.81
7.5 – 2.81 = 4.69
7.5 – 2.89 = 4.61
7.5 – 4.61 = 2.89
7.5 – 4.69 = 2.81
7.5 – 4.81 = 2.69
7.5 – 4.89 = 2.61
7.8 – 2.31 = 5.49
7.8 – 2.39 = 5.41
7.8 – 2.41 = 5.39
7.8 – 2.49 = 5.31
7.8 – 3.21 = 4.59
7.8 – 3.29 = 4.51
7.8 – 3.51 = 4.29
7.8 – 3.59 = 4.21
7.8 – 4.21 = 3.59
7.8 – 4.29 = 3.51
7.8 – 4.51 = 3.29
7.8 – 4.59 = 3.21
7.8 – 5.31 = 2.49
7.8 – 5.39 = 2.41
7.8 – 5.41 = 2.39
7.8 – 5.49 = 2.31
7.9 – 1.32 = 6.58
7.9 – 1.38 = 6.52
7.9 – 1.52 = 6.38
7.9 – 1.58 = 6.32
7.9 – 6.32 = 1.58
7.9 – 6.38 = 1.52
7.9 – 6.52 = 1.38
7.9 – 6.58 = 1.32
8.1 – 2.34 = 5.76
8.1 – 2.36 = 5.74
8.1 – 2.43 = 5.67
8.1 – 2.47 = 5.63
8.1 – 2.63 = 5.47
8.1 – 2.67 = 5.43
8.1 – 2.74 = 5.36
8.1 – 2.76 = 5.34
8.1 – 5.34 = 2.76
8.1 – 5.36 = 2.74
8.1 – 5.43 = 2.67
8.1 – 5.47 = 2.63
8.1 – 5.63 = 2.47
8.1 – 5.67 = 2.43
8.1 – 5.74 = 2.36
8.1 – 5.76 = 2.34
8.2 – 3.51 = 4.69
8.2 – 3.59 = 4.61
8.2 – 3.61 = 4.59
8.2 – 3.69 = 4.51
8.2 – 4.51 = 3.69
8.2 – 4.59 = 3.61
8.2 – 4.61 = 3.59
8.2 – 4.69 = 3.51
8.4 – 2.61 = 5.79
8.4 – 2.69 = 5.71
8.4 – 2.71 = 5.69
8.4 – 2.79 = 5.61
8.4 – 5.61 = 2.79
8.4 – 5.69 = 2.71
8.4 – 5.71 = 2.69
8.4 – 5.79 = 2.61
8.7 – 3.21 = 5.49
8.7 – 3.29 = 5.41
8.7 – 3.41 = 5.29
8.7 – 3.49 = 5.21
8.7 – 5.21 = 3.49
8.7 – 5.29 = 3.41
8.7 – 5.41 = 3.29
8.7 – 5.49 = 3.21
8.9 – 1.34 = 7.56
8.9 – 1.36 = 7.54
8.9 – 1.54 = 7.36
8.9 – 1.56 = 7.34
8.9 – 3.14 = 5.76
8.9 – 3.16 = 5.74
8.9 – 3.74 = 5.16
8.9 – 3.76 = 5.14
8.9 – 5.14 = 3.76
8.9 – 5.16 = 3.74
8.9 – 5.74 = 3.16
8.9 – 5.76 = 3.14
8.9 – 7.34 = 1.56
8.9 – 7.36 = 1.54
8.9 – 7.54 = 1.36
8.9 – 7.56 = 1.34
9.1 – 3.24 = 5.86
9.1 – 3.26 = 5.84
9.1 – 3.42 = 5.68
9.1 – 3.48 = 5.62
9.1 – 3.62 = 5.48
9.1 – 3.68 = 5.42
9.1 – 3.84 = 5.26
9.1 – 3.86 = 5.24
9.1 – 5.24 = 3.86
9.1 – 5.26 = 3.84
9.1 – 5.42 = 3.68
9.1 – 5.48 = 3.62
9.1 – 5.62 = 3.48
9.1 – 5.68 = 3.42
9.1 – 5.84 = 3.26
9.1 – 5.86 = 3.24
9.2 – 1.34 = 7.86
9.2 – 1.36 = 7.84
9.2 – 1.84 = 7.36
9.2 – 1.86 = 7.34
9.2 – 7.34 = 1.86
9.2 – 7.36 = 1.84
9.2 – 7.84 = 1.36
9.2 – 7.86 = 1.34
9.4 – 2.53 = 6.87
9.4 – 2.57 = 6.83
9.4 – 2.83 = 6.57
9.4 – 2.87 = 6.53
9.4 – 3.62 = 5.78
9.4 – 3.68 = 5.72
9.4 – 3.72 = 5.68
9.4 – 3.78 = 5.62
9.4 – 5.62 = 3.78
9.4 – 5.68 = 3.72
9.4 – 5.72 = 3.68
9.4 – 5.78 = 3.62
9.4 – 6.53 = 2.87
9.4 – 6.57 = 2.83
9.4 – 6.83 = 2.57
9.4 – 6.87 = 2.53
9.5 – 2.14 = 7.36
9.5 – 2.16 = 7.34
9.5 – 2.34 = 7.16
9.5 – 2.36 = 7.14
9.5 – 7.14 = 2.36
9.5 – 7.16 = 2.34
9.5 – 7.34 = 2.16
9.5 – 7.36 = 2.14
9.7 – 3.12 = 6.58
9.7 – 3.18 = 6.52
9.7 – 3.52 = 6.18
9.7 – 3.58 = 6.12
9.7 – 6.12 = 3.58
9.7 – 6.18 = 3.52
9.7 – 6.52 = 3.18
9.7 – 6.58 = 3.12
9.8 – 4.13 = 5.67
9.8 – 4.17 = 5.63
9.8 – 4.63 = 5.17
9.8 – 4.67 = 5.13
9.8 – 5.13 = 4.67
9.8 – 5.17 = 4.63
9.8 – 5.63 = 4.17
9.8 – 5.67 = 4.13
Solution with lowest result: 5.9 – 4.67 = 1.23
Solution with greatest result: 9.2 – 1.34 = 7.86
Two of my 5th graders found the following solution: 9.5 – 7.14 = 2.36, great job boys!