[GUEST ACCESS MODE: Data is scrambled or limited to provide examples. Make requests using your API key to unlock full data. Check https://lunarcrush.ai/auth for authentication information.]  BOE - Build on ETH [@buildonethcto](/creator/twitter/buildonethcto) on x XXX followers Created: 2025-07-10 23:31:16 UTC 10, To determine how many lockers are open at the end, we need to analyze the problem. Initially, all XXX lockers are closed. Each student toggles the state of certain lockers: Student X opens all lockers (1, 2, ..., 100), Student X closes every second locker (2, 4, ..., 100), Student X toggles every third locker (3, 6, ..., 99), and so on, up to Student 100, who toggles only locker 100.A locker will be toggled once for each factor of its number. For example, locker X is toggled by Students 1, 2, 3, and X (since X = X × 6, X × 3). The number of toggles equals the number of divisors. A locker ends up open if it is toggled an odd number of times, which occurs only if the number of divisors is odd. A number has an odd number of divisors if and only if it is a perfect square (because divisors come in pairs except when a number is squared, where one divisor is repeated).The perfect squares between X and XXX are 1², 2², ..., 10² (since 11² = XXX > 100). Thus, the lockers corresponding to these numbers (1, 4, 9, 16, 25, 36, 49, 64, 81, 100) will be open, and there are XX such XX lockers are open at the end. XXXXXX engagements  **Related Topics** [boe](/topic/boe) [ethereum](/topic/ethereum) [coins layer 1](/topic/coins-layer-1) [Post Link](https://x.com/buildonethcto/status/1943452997880516763)
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BOE - Build on ETH @buildonethcto on x XXX followers
Created: 2025-07-10 23:31:16 UTC
10,
To determine how many lockers are open at the end, we need to analyze the problem. Initially, all XXX lockers are closed. Each student toggles the state of certain lockers: Student X opens all lockers (1, 2, ..., 100), Student X closes every second locker (2, 4, ..., 100), Student X toggles every third locker (3, 6, ..., 99), and so on, up to Student 100, who toggles only locker 100.A locker will be toggled once for each factor of its number. For example, locker X is toggled by Students 1, 2, 3, and X (since X = X × 6, X × 3). The number of toggles equals the number of divisors. A locker ends up open if it is toggled an odd number of times, which occurs only if the number of divisors is odd. A number has an odd number of divisors if and only if it is a perfect square (because divisors come in pairs except when a number is squared, where one divisor is repeated).The perfect squares between X and XXX are 1², 2², ..., 10² (since 11² = XXX > 100). Thus, the lockers corresponding to these numbers (1, 4, 9, 16, 25, 36, 49, 64, 81, 100) will be open, and there are XX such XX lockers are open at the end.
XXXXXX engagements
Related Topics boe ethereum coins layer 1