Question

Isabella 有 $6$ 张优惠券，可以在 Pete's Sweet Treats 兑换免费冰淇淋筒。为了让优惠券用得久一些，她决定每隔 $10$ 天兑换一张，直到全部用完。她知道 Pete's 星期日关门，但当她在日历上圈出这 $6$ 个日期时，发现没有一个圈出的日期是星期日。Isabella 第一次兑换优惠券是在星期几？

Isabella has $6$ coupons that can be redeemed for free ice cream cones at Pete's Sweet Treats. In order to make the coupons last, she decides that she will redeem one every $10$ days until she has used them all. She knows that Pete's is closed on Sundays, but as she circles the $6$ dates on her calendar, she realizes that no circled date falls on a Sunday. On what day of the week does Isabella redeem her first coupon?

星期一

Monday

星期二

Tuesday

星期三

Wednesday

星期四

Thursday

星期五

Friday

答案：C

知识点：模运算日期与时间

难度评级：1310

视频讲解：

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文字解答：

逐个检查选项即可。

每隔 $10$ 天兑换一次，星期几会前进 $3$ 天。

若第一次是星期 $x$ ，六次兑换的星期依次为 $x, x+3, x+6, x+2, x+5$ 和 $x+1$ （模 $7$ ）。

唯一没出现的是 $x+4$ ，所以星期日必须在第一次兑换日后四天。星期日前四天是星期三。

正确答案是 C。

Let us go through the answer choices.

Each redemption is $10$ days later, which advances the weekday by $3$ days.

Starting on day $x,$ the six redemption days are $x, x+3, x+6, x+2, x+5,$ and $x+1$ modulo $7.$

The only missed weekday is $x+4,$ so Sunday must be four days after the first redemption day. Four days before Sunday is Wednesday.

Thus, the correct answer is C.

2019 AMC 8 第 14 题

答案：C

难度评级：1310

视频讲解：

文字解答：

其他年份的第 14 题