Open Middle®
Directions: Using the digits 1 to 9, at most one time each, make the following statement true.
Hint
How can you make the hundredths a tenth?
Answer
There are many solutions that sum to 9 4.87+2.63+1.5=9, 2.83 + 4.57 + 1.6 = 9.
Source: Miles Knight
1.41+1.09+1.5=4
You can only use each digit once though, Alejandro.
1,5+2,7+3,8=8
4.25+3.15+1.6=9
You are using 5 and 1 more than once
i agree
Me too! good answer, sofia.
me too as in i agree too
All the solutions have (1,2,4) in the ones place, (5,6,8) in the tenths place, (3,7) in the hundredths place, and 9 as the whole number sum. For example, 1.53 + 2.67 + 4.8 = 9. There are 36 solutions, I think, and they all fit this pattern. Starting from the fact that the whole number must be 9, then the ones place digits must sum to 7, the tenths place digits must sum to 19, and the hundredths place digits must sum to 10. There’s only one way to get those sums.
Fun problem! I approached it the same way as I did https://www.openmiddle.com/close-to-1000/
Good explanation, Brian. Thank you.
Yup, 36 solutions.
1.53 + 2.67 + 4.8 = 9
1.53 + 2.87 + 4.6 = 9
1.53 + 4.67 + 2.8 = 9
1.53 + 4.87 + 2.6 = 9
1.57 + 2.63 + 4.8 = 9
1.57 + 2.83 + 4.6 = 9
1.57 + 4.63 + 2.8 = 9
1.57 + 4.83 + 2.6 = 9
1.63 + 2.57 + 4.8 = 9
1.63 + 2.87 + 4.5 = 9
1.63 + 4.57 + 2.8 = 9
1.63 + 4.87 + 2.5 = 9
1.67 + 2.53 + 4.8 = 9
1.67 + 2.83 + 4.5 = 9
1.67 + 4.53 + 2.8 = 9
1.67 + 4.83 + 2.5 = 9
1.83 + 2.57 + 4.6 = 9
1.83 + 2.67 + 4.5 = 9
1.83 + 4.57 + 2.6 = 9
1.83 + 4.67 + 2.5 = 9
1.87 + 2.53 + 4.6 = 9
1.87 + 2.63 + 4.5 = 9
1.87 + 4.53 + 2.6 = 9
1.87 + 4.63 + 2.5 = 9
2.53 + 4.67 + 1.8 = 9
2.53 + 4.87 + 1.6 = 9
2.57 + 4.63 + 1.8 = 9
2.57 + 4.83 + 1.6 = 9
2.63 + 4.57 + 1.8 = 9
2.63 + 4.87 + 1.5 = 9
2.67 + 4.53 + 1.8 = 9
2.67 + 4.83 + 1.5 = 9
2.83 + 4.57 + 1.6 = 9
2.83 + 4.67 + 1.5 = 9
2.87 + 4.53 + 1.6 = 9
2.87 + 4.63 + 1.5 = 9
Plus another 36 if you swap the first two addends
I did 3000 x 39847
It says you use the numbers at most, 1 time each but it doesn’t require you to use them. Therefore, I have 6.32 + .5 + .18 = 7.
Three of my students got this. Here is there answer-
Noah and Cormac. 1.87 + 4.53 + 2.6 = 9
Ava 4.83 + 2.57 + 1.6 = 9