Math Problem with 6’s from Scam School

TestTube^TM is a new digital network from Discovery^TM. With shows like Stuff of Genius, Blow It Up!, and Distort (where “great ideas become reality”), it holds strong appeal for mathy folks.

My favorite show on TestTube^TM is Scam School, where magician Brian Blushwood takes you on a tour of bar tricks, street cons, and scams. In the episode “Six the Hard Way,” he poses a mathematical challenge that is a variation on one you may have seen before. As Brian explains, “it’s almost poetic how simple this is.”

The puzzle is this: Form an expression with three 1’s, three 2’s, three 3’s, and so on, up to three 9’s, so that the value of each expression is equal to 6. As an example, an expression using three 7’s is shown below. Can you find expressions using the other numbers?

0   0   0 = 6

1   1   1 = 6

2   2   2 = 6

3   3   3 = 6

4   4   4 = 6

5   5   5 = 6

6   6   6 = 6

7 – 7 ÷ 7 = 6

8   8   8 = 6

9   9   9 = 6

You can watch Six the Hard Way, but be forewarned: at least one solution for each number is given, so you may want to solve the puzzle before viewing.

Also note that some folks have posted solutions in the comments below, so scroll at your own risk.