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
How do you place digits so the sum is less than ten?
Answer
There are 160 unique solutions. Three examples are:
1: 1.2 + 3.5 = 4.7
2: 1.5 + 6.3 = 7.8
3: 2.1 + 5.3 = 7.4
1: 1.2 + 3.5 = 4.7
2: 1.5 + 6.3 = 7.8
3: 2.1 + 5.3 = 7.4
Source: Owen Kaplinsky
My fifth grade student was super proud she found 9 ways so far to complete this! She wanted me to post it here . Thanks!
I found out 20 ways to do this problem! Here are some ways:
4.8+3.1=7.9
3.2+4.7=7.9
7.1+2.3=9.4
1.5+2.4=3.9
8.3+1.4=9.7
I am in 5th grade and i found 3.4+5.2=8.6
I am in 4th grade and going to fifth grade after summer break. I found a lot of ways, on of them is 1.4+6.5=7.9
I am in Sixth grade and this is so good and fun to solve
The directions say to make “two true statements”, but it’s not possible to make two such statements each using 6 digits and have no digit be repeated. I guess the directions should say “to make *a* true statement”
The “solution”-section is missing a lot of solutions. There are 200 solutions, not just 160:
1.2 + 3.5 = 4.7
1.2 + 3.6 = 4.8
1.2 + 3.7 = 4.9
1.2 + 4.6 = 5.8
1.2 + 4.7 = 5.9
1.2 + 5.7 = 6.9
1.2 + 6.3 = 7.5
1.2 + 7.3 = 8.5
1.2 + 7.4 = 8.6
1.2 + 8.3 = 9.5
1.2 + 8.4 = 9.6
1.2 + 8.5 = 9.7
1.3 + 4.6 = 5.9
1.3 + 4.9 = 6.2
1.3 + 5.4 = 6.7
1.3 + 5.9 = 7.2
1.3 + 6.2 = 7.5
1.3 + 6.5 = 7.8
1.3 + 6.9 = 8.2
1.3 + 7.2 = 8.5
1.3 + 7.6 = 8.9
1.3 + 8.2 = 9.5
1.3 + 8.4 = 9.7
1.4 + 2.5 = 3.9
1.4 + 3.8 = 5.2
1.4 + 5.3 = 6.7
1.4 + 5.8 = 7.2
1.4 + 5.9 = 7.3
1.4 + 6.5 = 7.9
1.4 + 6.9 = 8.3
1.4 + 7.2 = 8.6
1.4 + 7.5 = 8.9
1.4 + 7.8 = 9.2
1.4 + 8.2 = 9.6
1.4 + 8.3 = 9.7
1.5 + 2.4 = 3.9
1.5 + 2.8 = 4.3
1.5 + 3.2 = 4.7
1.5 + 4.7 = 6.2
1.5 + 4.8 = 6.3
1.5 + 6.3 = 7.8
1.5 + 6.4 = 7.9
1.5 + 6.7 = 8.2
1.5 + 6.9 = 8.4
1.5 + 7.4 = 8.9
1.5 + 7.8 = 9.3
1.5 + 8.2 = 9.7
1.6 + 2.7 = 4.3
1.6 + 2.9 = 4.5
1.6 + 3.2 = 4.8
1.6 + 3.8 = 5.4
1.6 + 4.2 = 5.8
1.6 + 4.3 = 5.9
1.6 + 5.8 = 7.4
1.6 + 7.3 = 8.9
1.6 + 7.8 = 9.4
1.7 + 2.6 = 4.3
1.7 + 2.8 = 4.5
1.7 + 2.9 = 4.6
1.7 + 3.2 = 4.9
1.7 + 3.9 = 5.6
1.7 + 4.2 = 5.9
1.7 + 4.5 = 6.2
1.7 + 4.8 = 6.5
1.7 + 5.2 = 6.9
1.7 + 6.5 = 8.2
1.8 + 2.5 = 4.3
1.8 + 2.7 = 4.5
1.8 + 2.9 = 4.7
1.8 + 3.4 = 5.2
1.8 + 3.6 = 5.4
1.8 + 3.9 = 5.7
1.8 + 4.5 = 6.3
1.8 + 4.7 = 6.5
1.8 + 4.9 = 6.7
1.8 + 5.4 = 7.2
1.8 + 5.6 = 7.4
1.8 + 7.4 = 9.2
1.8 + 7.5 = 9.3
1.8 + 7.6 = 9.4
1.9 + 2.6 = 4.5
1.9 + 2.7 = 4.6
1.9 + 2.8 = 4.7
1.9 + 3.7 = 5.6
1.9 + 3.8 = 5.7
1.9 + 4.3 = 6.2
1.9 + 4.8 = 6.7
1.9 + 5.3 = 7.2
1.9 + 5.4 = 7.3
1.9 + 6.3 = 8.2
1.9 + 6.4 = 8.3
1.9 + 6.5 = 8.4
2.1 + 3.6 = 5.7
2.1 + 3.7 = 5.8
2.1 + 3.8 = 5.9
2.1 + 4.7 = 6.8
2.1 + 4.8 = 6.9
2.1 + 5.3 = 7.4
2.1 + 5.8 = 7.9
2.1 + 6.3 = 8.4
2.1 + 6.4 = 8.5
2.1 + 7.3 = 9.4
2.1 + 7.4 = 9.5
2.1 + 7.5 = 9.6
2.3 + 4.5 = 6.8
2.3 + 4.8 = 7.1
2.3 + 5.1 = 7.4
2.3 + 5.6 = 7.9
2.3 + 6.1 = 8.4
2.3 + 6.4 = 8.7
2.3 + 6.8 = 9.1
2.3 + 7.1 = 9.4
2.3 + 7.5 = 9.8
2.4 + 3.7 = 6.1
2.4 + 5.7 = 8.1
2.4 + 5.9 = 8.3
2.4 + 6.1 = 8.5
2.4 + 6.3 = 8.7
2.4 + 6.5 = 8.9
2.4 + 6.7 = 9.1
2.4 + 7.1 = 9.5
2.5 + 3.9 = 6.4
2.5 + 4.3 = 6.8
2.5 + 4.6 = 7.1
2.5 + 4.8 = 7.3
2.5 + 6.4 = 8.9
2.5 + 6.8 = 9.3
2.5 + 7.1 = 9.6
2.5 + 7.3 = 9.8
2.6 + 3.1 = 5.7
2.6 + 4.5 = 7.1
2.6 + 4.9 = 7.5
2.6 + 5.3 = 7.9
2.6 + 5.7 = 8.3
2.7 + 3.1 = 5.8
2.7 + 3.4 = 6.1
2.7 + 3.8 = 6.5
2.7 + 4.1 = 6.8
2.7 + 5.4 = 8.1
2.7 + 5.6 = 8.3
2.7 + 5.9 = 8.6
2.7 + 6.4 = 9.1
2.7 + 6.8 = 9.5
2.8 + 3.1 = 5.9
2.8 + 3.7 = 6.5
2.8 + 3.9 = 6.7
2.8 + 4.1 = 6.9
2.8 + 4.3 = 7.1
2.8 + 4.5 = 7.3
2.8 + 5.1 = 7.9
2.8 + 6.3 = 9.1
2.8 + 6.5 = 9.3
2.8 + 6.7 = 9.5
2.9 + 3.5 = 6.4
2.9 + 3.8 = 6.7
2.9 + 4.6 = 7.5
2.9 + 5.4 = 8.3
2.9 + 5.7 = 8.6
3.1 + 4.5 = 7.6
3.1 + 4.8 = 7.9
3.1 + 5.6 = 8.7
3.1 + 6.4 = 9.5
3.1 + 6.7 = 9.8
3.2 + 4.6 = 7.8
3.2 + 4.9 = 8.1
3.2 + 5.4 = 8.6
3.2 + 5.7 = 8.9
3.2 + 6.5 = 9.7
3.4 + 5.2 = 8.6
3.4 + 5.7 = 9.1
3.4 + 5.8 = 9.2
3.4 + 6.1 = 9.5
3.5 + 4.1 = 7.6
3.5 + 4.6 = 8.1
3.5 + 4.7 = 8.2
3.5 + 6.2 = 9.7
3.6 + 4.2 = 7.8
3.6 + 4.5 = 8.1
3.6 + 4.9 = 8.5
3.6 + 5.1 = 8.7
3.6 + 5.8 = 9.4
3.7 + 4.5 = 8.2
3.7 + 4.9 = 8.6
3.7 + 5.2 = 8.9
3.7 + 5.4 = 9.1
3.7 + 6.1 = 9.8
3.8 + 4.1 = 7.9
3.8 + 5.4 = 9.2
3.8 + 5.6 = 9.4
3.9 + 4.2 = 8.1
3.9 + 4.6 = 8.5
3.9 + 4.7 = 8.6
4.1 + 5.2 = 9.3
4.1 + 5.6 = 9.7
4.1 + 5.7 = 9.8
4.2 + 5.1 = 9.3
4.2 + 5.6 = 9.8
4.6 + 5.1 = 9.7
4.6 + 5.2 = 9.8
4.7 + 5.1 = 9.8
The “solution”-section for example has 2.5 + 1.8 = 4.3, 2.6 + 1.7 = 4.3, 2.8 + 1.5 = 4.3 but is missing 2.7 + 1.6 = 4.3.
Cool, 3.4 + 5.2 = 8.6 would work right?
I found so many ways, maybe 14