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First Round

Netherlands counting and probability

Problem

Lieneke is making bracelets with beads. Each bracelet has six beads: two white, two grey, and two black beads. Some bracelets look different on first sight, but are actually not different: by turning or flipping the first one over, it looks the same as the other one. For example, the following three bracelets are the same.
problem
problem
problem
How many really different bracelets can Lieneke make? A) 10 B) 11 C) 12 D) 14 E) 15
Solution
B) 11
Final answer
B) 11

Techniques

Enumeration with symmetry