Library / CEMC Gauss (Grade 8) /461 of 525

CEMC Gauss (Grade 8), 2000

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer Canada

A square floor is tiled, as partially shown, with a large number of regular hexagonal tiles. The tiles are coloured blue or white. Each blue tile is surrounded by $6$ white tiles and each white tile is surrounded by $3$ white and $3$ blue tiles. Ignoring part tiles, the ratio of the number of blue tiles to the number of white tiles is closest to

(A) $1:6$ (B) $2:3$ (C) $3:10$ (D) $1:4$ (E) $1:2$

Figure for this problem

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.