Open Middle®
Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to create the smallest possible difference.
Hint
Remember that zeros are not allowed. Because you can only use each digit once, the digit in the hundreds place can’t be the same.
Answer
14
One possible solution is 612-598 = 14.
Source: Graham Fletcher
We also got 14 with 412-398=14.
Nice!
999-987
nice!
But you used 1 in the question and 1 in the answer.
The answer isn’t included in the digits being used once, since it says “fill the boxes”.
My best is 718-695 = 23
612-598=14.
612-598=14
612-598 = 14
612-598=14
612-598=14
612-598=14
412-398=14
512-498=14
512-498=14
My best is 701-698=3
You cannot use the number 0
516-498=18
You cannot use the number 0 in the problem.
612-598=14
516-498=18
612-598=14
612-598=14
987-987=0
you can’t repeat the same numbers
102-96=2
So no repeating numbers and no zero and the answer is fine.
Well no using the same numbers twice.
Smallest difference is 14. Possible combinations are: 812-798, 712-698, 612-598, 512-498 and 412-398.
Largest difference is 987-123=864
Largest difference – so you can have repeat numbers in the problem and in the answer?
976-853=123
912-865=47
123-987= -864
861-759=2
Oops! My bad!
My daughter is working on this exact math problem. Can anyone explain HOW you know to get to this answer?