The Hotel

The Holiday Hotel has the same number of rooms on each floor. Rooms are numbered with natural numbers sequentially from the first floor, no number is omitted, and each room has a different number. Three tourists arrived at the hotel. The first one was in room number 50 on the fourth floor. The other room number 100 on the seventh floor, third in room number 126 on the ninth floor. How many rooms are on each floor?

Result

n =  15

Solution:

0503n<n 01006n<n 01268n<n  50<4n100<7n126<9n 12.5<n14.28<n14<n  n16.666n16.666n15.75  1007<n634 nN n=150 \leq 50 - 3n<n \ \\ 0 \leq 100 - 6n<n \ \\ 0 \leq 126 - 8n<n \ \\ \ \\ 50 < 4n \land 100 < 7n \land 126 < 9n \ \\ 12.5 < n \land 14.28 < n \land 14 < n \ \\ \ \\ n \leq 16.666 \land n \leq 16.666 \land n \leq 15.75 \ \\ \ \\ \dfrac{ 100 }{ 7 } < n \leq \dfrac{ 63 }{ 4 } \ \\ n \in N \ \\ n=15



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