Open Middle®
Directions: Using the digits 0 to 9, at most one time each, place a digit in each box to find a sum where all the digits are the same. What is the greatest sum? What is the least sum?
Hint
Consider addends that require regrouping.
What is the relationship between the digit in the hundredths place and the sum?
What could the possible sums be? What sums don’t work?
What is the relationship between the digit in the hundredths place and the sum?
What could the possible sums be? What sums don’t work?
Answer
There are many solutions. Four examples are:
1. 0.34 + 1.6 + 2.5 = 4.44
2. 1.07 + 2.8 + 3.9 = 7.77
3. 6.48 + 2.3 + 0.1 = 8.88
4. 2.89 + 4.1 + 3.0 = 9.99
1. 0.34 + 1.6 + 2.5 = 4.44
2. 1.07 + 2.8 + 3.9 = 7.77
3. 6.48 + 2.3 + 0.1 = 8.88
4. 2.89 + 4.1 + 3.0 = 9.99
The only possible sums are for 4.44, 7.77, 8.88, 9.99, 11.11, and 22.22.
Source: Elizabeth Trochil
Our Grade 5 class found many solutions to this problem – we enjoyed it! They would like to share that they believe 22.22 is the greatest sum that is possible, since the next sums with the same digits would be 33.33 and it is impossible to reach 33 with the whole numbers. Some of the ways we got to 22.22 are: 9.62 + 8.5 + 3.1 = 22.22 and 6.32+ 8.5 + 7.4 = 22.22
They also think that 4.44 is the smallest sum you can get since it is impossible to get 3.33. We found 1.64 + 2.3 + 0.5.
We found solutions for 4.44, 7.77, 8.88., 9.99, 11.11 and 22.22 but not for 6.66 or 5.55 – we wonder if these are still possible?
Hello FiveDvM Dragons! We are a fifth grade class in Denver and we are the Park Hill Panthers!
We found a similar greatest sum of 22.2 but appreciated seeing your 22.22!
We did find that 0.75 + 3.6 + 1.2 = 5.55
We also enjoyed the problem! Thanks Open Middle!
0.32 + 079 = 1.11
Digits used: 0, 3, 2, 7, 9, 1 → total of 6 digits
Total is 1.11 → only uses digit 1
Answer = 9.99
anser 9.99
=9.99