Unconventional dice are to be designed such that the six faces are marked with numbers from 1 to 6 w

Question

Unconventional dice are to be designed such that the six faces are marked with numbers from 1 to 6 with 1 and 2 appearing on opposite faces. Further, each face is colored either red or yellow with opposite faces always of the same color. Two dice are considered to have the same design if one of them can be rotated to obtain a dice that has the same numbers and colors on the corresponding faces as the other one. Find the number of distinct dice that can be designed

Accepted Answer

{"content":[{"content":[{"marks":[{"type":"bold"}],"text":"Step 1:","type":"text"},{"type":"text","text":" Fix 1 and 2 anywhere in 1 way"}],"type":"paragraph"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 2:","type":"text"},{"text":" Fix 3 anywhere in 1 way","type":"text"}],"type":"paragraph"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 3:","type":"text"},{"text":" 1           2","type":"text"}],"type":"paragraph"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 4:","type":"text"},{"type":"text","text":" Now remaining 3 faces can be filled in       ways and coloring them in 2 × 2 × 2 ways"}],"type":"paragraph"},{"content":[{"text":"Step 5:","type":"text","marks":[{"type":"bold"}]},{"text":" =>     Total distinct dice =      × 8 = 24 ways","type":"text"}],"type":"paragraph"}],"type":"doc"}

Guide / Hint

Solution