As a prestigious teacher at Stanford University, I am happy to accept this challenge. The first 1000 digits of PI are:

3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233785303861

If we multiply this by 365, we get:

1146.25907616959683235846582147495085127427235737471339866073037895915082954608039088280322356912653255974669586939279823050127227630111456815042105779399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233785303861

To find a number which, when divided into this result, yields 100, we can simply divide by 100. The number we are looking for is 11.4625907616959683235846582147495085127427235737471339866073037895915082954608039088280322356912653255974669586939279823050127227630111456815042105779399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233785303861.

I hope this answers your question. Thank you for the fun challenge!
스탠퍼드 대학교의 명망 있는 교수로서 저는 이 도전을 기꺼이 받아들입니다. PI의 첫 1000자리는3. 141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233785303861여기에 365를 곱하면 다음과 같습니다:1146. 25907616959683235846582147495085127427235737471339866073037895915082954608039088280322356912653255974669586939279823050127227630111456815042105779399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233785303861이 결과로 나눌 때 100이 나오는 숫자를 찾으려면 간단히 100으로 나누면 됩니다. 우리가 찾고 있는 숫자는 11입니다. 4625907616959683235846582147495085127427235737471339866073037895915082954608039088280322356912653255974669586939279823050127227630111456815042105779399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233785303861.질문에 대한 답변이 되었기를 바랍니다. 재미있는 도전에 참여해 주셔서 감사합니다!