分针每分钟走6°,时针每分钟走0.5°.
n点m分【特别注意：0≤m＜60】,时针与分针成90度的角,必须满足
或 6m-(30n+0.5m)=90 ①
或 (30n+0.5m)-6m=90 ②
或 6m-(30n+0.5m)=270 ③
或 (30n+0.5m)-6m=270 ④
① 6m-(30n+0.5m)=90 ===> m=(180+60n)/11,
仅当n=0,1,2,3,4,5,6,7时,才满足0≤m＜60.
② (30n+0.5m)-6m=50 ===> m=(60n-180)/11.
仅当n=4,5,6,7,8,9,10,11时,才满足0≤m＜60.
③ 6m-(30n+0.5m)=270 ===> m=(540+60n)/11.
当n=0,1时,才满足0≤m＜60.
④ (30n+0.5m)-6m=270 ===> m=(60n-540)/11,
当n=10,11时,才满足0≤m＜60.
0:00～12:00时针与分针成90°角共有20次.