分針每分鐘走6°,時(shí)針每分鐘走0.5°.
n點(diǎn)m分【特別注意：0≤m＜60】,時(shí)針與分針成90度的角,必須滿足
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,
僅當(dāng)n=0,1,2,3,4,5,6,7時(shí),才滿足0≤m＜60.
② (30n+0.5m)-6m=50 ===> m=(60n-180)/11.
僅當(dāng)n=4,5,6,7,8,9,10,11時(shí),才滿足0≤m＜60.
③ 6m-(30n+0.5m)=270 ===> m=(540+60n)/11.
當(dāng)n=0,1時(shí),才滿足0≤m＜60.
④ (30n+0.5m)-6m=270 ===> m=(60n-540)/11,
當(dāng)n=10,11時(shí),才滿足0≤m＜60.
0:00～12:00時(shí)針與分針成90°角共有20次.