Open Middle®
Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to make true statements. For the fraction less than 1/2, try to make the greatest number possible. For the fraction greater than 1/2, try to make the least number possible.
Hint
How can you use the digits you have remaining to create a fraction that equals 1/2?
Answer
There are 394 unique solutions. Three examples are:
1: 1/3 < 1/2 and 4/6 > 1/2 and 29/58 = 1/2
2: 1/3 < 1/2 and 4/7 > 1/2 and 28/56 = 1/2
3: 1/3 < 1/2 and 4/7 > 1/2 and 29/58 = 1/2
1: 1/3 < 1/2 and 4/6 > 1/2 and 29/58 = 1/2
2: 1/3 < 1/2 and 4/7 > 1/2 and 28/56 = 1/2
3: 1/3 < 1/2 and 4/7 > 1/2 and 29/58 = 1/2
Source: Alyson Eaglen
1/5 1/2 and 22/44= 1/2
1/3 1/2 and 48/96 = 1/2
3/9 1/2 and 14/28 = 1/2
14>12and 47>12and 20 100 >12
1/5 1/2 7/9 1/2 34/68=1/2
1/3 1/2 and 22/44 = 1/2
1/41/2 and 1/4+1/4=1/2
4/91/2 and 13/26=1/2
Answer: 373
It works
1/2 1/2 and 2/3 1/2 and 3/4 4/5=1/2
1/41/2 and 24/48=1/2
3/8 1/2 and 47/92 = 1/2