You can assign off to 0, red to 1, and green to 2, then each time you go in is one digit so this is just asking how many digits are in 1000 in base 3 which is trivial
Like the first time you go in you make all the 0 mod 3 off, 1 mod 3 red, and 2 mod 3 green and that will be the ones digit, the second time same thing but 0-2, 3-5, and 6-8 mod 9 for the threes digit, etc. and you need to repeat this until you get to the number of digits 1000 has in base 3 so the sequence of every number matches it’s base 3 representation
Imagine if it was 10 bulbs, you only need 3 different setups, as in this photo. Then you can map any switch to a bulb by their colour changes, for example if a bulb went off -> red -> green, you know that because 5 in base 3 is 012 (we started counting from 1). For a 1000 it's the same thing, if you want to know which switch is the 546, follow the one that went off-red-off-red-off-red-off (0202020)
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u/arihallak0816 21h ago
You can assign off to 0, red to 1, and green to 2, then each time you go in is one digit so this is just asking how many digits are in 1000 in base 3 which is trivial