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Can you guys help me or give me a hint just this once. Im in a tight spot
3. [10 pts] In an attempt to get in with the cool kids, Bharath decides to make Vivian a charm
necklace. After some careful research into her preferences, he noticed that she likes her necklaces
to be symmetrical but doesn’t want any two charms next to each other to have the same color.
In addition, Vivian only likes necklaces that have 13 charms.
In his extensive collection, Bharath has charms in 4 shapes (stars, hearts, ovals, and crescent
moons) and 4 colors (red, blue, pink, and chartreuse). He has 100 of each possible charm (so
1600 charms in total). How many different necklaces could Bharath possibly make to win her
over?
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Willng to trade
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For a necklace to be symmetrical you can just make a string of seven unique beads and reflect six of them in a row and append them to the original seven. So you can have the middle of the thirteen beads be any of the sixteen kinds of bead. The next one can be one of twelve, since it can't be the same colour. The one after that can be one of twelve, and so on. (Cont.)
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Scratch that entire previous post. What does it even mean to be symmetrical, you mean the bead types, or colour, or what? If it needs to have symmetrical colour on a closed necklace I don't think it is possible.
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>>8632423
Not OP, but I assume it just means the bead shape and color must be the same symmetrically across the middle bead. So if the left end is a red star then the right-most end is a red-star and so on.
This sounds like a subset problem where you choose subsets of 6 and then multiply the result by 12 (the middle bead which can't be the same color as the ones next to it).
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>>8630532
Do you know the answer? I think it's 4455360
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