More Than Enough to Fill It Up

Probability Level pending

How many ways are there to fill up the rest of the square grid with purple, pink, blue and yellow squares, such that each row and each column contains at most 1 square of each color?

1 2 4 8

2 solutions

Hana Wehbi
Apr 9, 2016

Graph theory, choosing colors so that no edge shares same color from both squares. And:4

Hm, can you provide more details and share your working? Thanks!

Calvin Lin Staff - 5 years, 2 months ago

I solved this by only using colors to the empty squares and noticed only 4 are needed.

Hana Wehbi - 5 years, 2 months ago

I'm curious, how does it relate to graph theory? Which ideas are you using?

Calvin Lin Staff - 5 years, 2 months ago

@Calvin Lin – Four color theorem: tells us that any map, no matter how large and complicated, can be colored using no more than four colors.

Hana Wehbi - 5 years, 2 months ago

@Hana Wehbi – Sure, but how does that apply to this problem? How does that tell us that there are 4 ways to complete the coloring?

Calvin Lin Staff - 5 years, 2 months ago

Calvin Lin Staff
Apr 8, 2016

(This is not a complete solution).

The answer to this problem is the same as the answer to the $4 \times 4$ grid

which is posted here .

Is there a reason why? Can we generalize this to larger squares?

More Than Enough to Fill It Up

2 solutions

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