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?

Answer: C

Concepts:modular arithmeticdate and time

Difficulty rating: 1310

AMC 8AMC 10AMC 12AIME

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Written solution:

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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.