Question 105
On each of 9 balls a distinct number chosen from 1 through 9 is marked. How many distinct ways of choosing some balls from this collection of 9 balls are there if the choice has to satisfy the following condition? Selecting no ball from the collection should be considered as 1 possibility.
**Condition:** By selecting suitably some balls from the chosen balls and putting them into a red box, and putting the remaining chosen balls into a blue box, we can make the difference of the numbers marked on any pair of balls in the same colored box to be 2 or less.
**Condition:** By selecting suitably some balls from the chosen balls and putting them into a red box, and putting the remaining chosen balls into a blue box, we can make the difference of the numbers marked on any pair of balls in the same colored box to be 2 or less.