Report Light bulb problem on steroids in New Logic/Math Puzzles Posted September 19, 2007 You can pose this puzzle with 10 bulbs instead of with 100. But then it's too easy to grind it out; boring. You can also pose it with 1000 bulbs. But life is short, and people with any sense walk away, and miss the fun. Michlips appears to be in that [sensible <!-- s;) --><!-- s;) --> ] group. The whole idea is to find the short cut; and grinding it out partially can light the way. ergo, 100 bulbs is only moderately complex and sucks you in to the search. KamZhiYhi took the first step and realized bulb #1 would be on - partial credit. unreality went farther, saw the pattern, and found the answer. Here's another way to see the solution. Observation 1. Switches flipped an odd number of times are left ON. Observation 2. Switch N is flipped once for each of its factors: [1,N], etc. Observation 3. Factors come in pairs, but for squares one factor is repeated. Solution: Squares are left ON, since they have an odd number of distinct factors. Factors of 8: [1,8], [2,4] - Persons 1,2,4 and 8 flipped switch 8. Even number of flips. Light is OFF. Factors of 9: [1,9], [3,3] - Persons 1,3 and 9 flipped switch 9. Odd number of flips. Light is ON.