Open Middle®
Directions: Using the digits 1 to 9 at most twice each, make the sum of the four expressions the greatest possible value.
Hint
Which calculation of the four can produce the greatest result?
Where should you place the greatest digits?
Which digits in the calculations need to be lesser value to give you a greater result?
Where should you place the greatest digits?
Which digits in the calculations need to be lesser value to give you a greater result?
Answer
Reading left to right, enter the digits in order:
6,7,6,7
4,5,2,1
8,9,8,9
4,5,2,1
6,7,6,7
4,5,2,1
8,9,8,9
4,5,2,1
Source: Catriona Shearer
great resources for teachers and students.
How can I make it interactive?
I got a little bit higher value using this instead:
6,7,6,7
4,5,2,2
8,9,8,9
4,5,1,1
Dividing by 10 in the division problem instead of 20 gave a difference of 20,000 to the final total. Of course, that doesn’t make much difference when your answer is 6.4 x 10^19
I love this! Thanks Catriona. I’m a huge fan of your geometry puzzles (from the most beautiful notebooks I’ve ever seen!) and it was great to see your name pop up here too