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## Tile A-While in Style

In the bag, place eight yellow tiles, seven red tiles, and five blue tiles.

Task: Without looking in the bag, what is the maximum number of tiles you can randomly remove ...and still be sure of leaving at least four tiles of one color?

Bigger Task: Can you generalize the problem:

• Start with same bag and starting tile counts, but you need to leave at least n tiles of one color, for n = 0, 1, 2, ..., 5?
• Start with y yellow tiles, r red tiles, and b blue tiles in the bag, but you need to leave at least n tiles of one color, for n = 0, 1, 2, ..., z (where z = min(y,r,b)?
• Start with (ti tiles of color ci in a big bag (all colors different), but you need to leave at least n tiles of one color, for n = 0, 1, 2, ..., z (where z = min(ti)?

Hint: Create the experiment.

Get a bag and given tile contents, start drawing tiles...record your data and thoughts...then use logical reasoning.

Solution Commentary: For the first task, does {[(255x478)+6]/15237}-1 look like the right answer?

NOTE: The above computations have no connection to the problem, other than to hide the possible answer somewhat!