Calling all Mathletes: Geof, our Engineering Team Lead, claims that he has discovered how many circuit combinations and permutations can be made with the littleBits Starter and Extended Kits. Does he look believable? We’re not sure, and we need your help.
littleBits is a library of electronic modules that snap together with tiny magnets. Each Bit is color-coded, blue is power, green is output, pink is input and orange is wire. Blue and green are required to make a circuit,
In every circuit…
-Power Bit always comes first (only one Power Bit per circuit)
-A circuit cannot be made without an Output Bit
-A circuit cannot have an Input Bit at the end
-A circuit cannot have a Wire Bit at end
-You cannot interchange the two Power Bits, the Wire Bits or the long LED Bits – they’re the same and do not constitute a new circuit
Consider that each littleBits Kit has…
x: Number of total Bits
i: Number of Input Bits
o: Number of Output Bits
w: Number of Wire Bits
p: Number of Power Bits
To use the Extended Kit as an example…
x = 14
i = 5
o = 5 (including 2 identical long LEDs)
w = 2 (including 2 identical Wire Bits)
p = 2 (including USB Power and Power Bit + Battery & Cable)
If you can figure out the correct number of circuits that can be made from the Starter Kit and the Extended Kit and show us how you arrived at that number in the comments, you can win $500 cash and $500 of Bits. Act fast – this contest ends Friday, July 26.
Good luck, Mathletes!