Let COL be a 3-coloring of the numbers 1, …, 2006. Show that there exist numbers X and Y such that COL(X) = COL(Y) and |X − Y| is a square. Appeared on Maryland Math Olympiad 2006. Acquired from Luca Trevisan’s blog.
3-coloring year 2006 - 2
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- 507 days 13 hours, Grigor commented on Crystal orbs: (Hope you still look at too old records. :-) ) Start at the square root of the...
- 510 days 8 hours, petar commented on 3-coloring year 2006: A 3-coloring is an assignment of one color (of possible three colors) to...
- 510 days 16 hours, Shubham commented on 3-coloring year 2006: What is a 3-colouring of numbers?
- 516 days 4 hours, petar commented on Approximating square roots: This problem has no “right” answer obviously, unless you...
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2 Comments ↓
What is a 3-colouring of numbers?
A 3-coloring is an assignment of one color (of possible three colors) to each number. So e.g. fix some three colors Red, Green and Blue and then a 3-coloring of the numbers 1, 2, 3, 4 and 5 could be say: 1->R, 2->G, 3->R, 4->B, 5->B.
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