With (2, 8) or (3, 9), and any other two numbers from 1 to 9, there is always a solution to the 24 Game.
Memories
I first found this when I was a kid and a beginner in programming 
. This result surprised me because I thought (2, 6), (4, 6) or (3, 8) were more likely to guarantee a solution.
After many years, as an old beginner now 
, I suddenly recall this conclusion and decide to write it down.
否则恐怕就再也不会回忆起来了……
Other fun facts
Let’s say the pair of numbers that guarantees a solution is “good”. If the numbers are chosen from 1 to
- 10 or higher: There is no good pair of numbers. Three numbers can be good though, and many solutions exist.
- 8: Only
(2, 8)and(4, 5)are good. - 7: Only
(4, 5)is good.
Btw, (4, 4, 6, 6), (3, 4, 8, 8) and (2, 2, 2, 6) have no solutions.