AIME竞赛真题分享来了 快拿真题来练手

马上就要进行AIME竞赛的考试了，相信有许多同学已经在复习了，为了让大家能够更加直观的了解到AIME竞赛的题型和考点，本期给大家带来几道AIME竞赛真题，同学们快来找感觉吧！

AIME竞赛真题

1 Find the number of positive integers with three not necessarily distinct digits, abc, with a 6= 0,c 6= 0 such that both abc and cba are divisible by 4.

2 The terms of an arithmetic sequence add to 715. The first term of the sequence is increased by 1, the second term is increased by 3, the third term is increased by 5, and in general, the kth term is increased by the kth odd positive integer. The terms of the new sequence add to 836.Find the sum of the first, last, and middle terms of the original sequence.

3 Nine people sit down for dinner where there are three choices of meals. Three people order the beef meal, three order the chicken meal, and three order the fish meal. The waiter serves the nine meals in random order. Find the number of ways in which the waiter could serve the meal types to the nine people such that exactly one person receives the type of meal ordered by that person.

4 Butch and Sundance need to get out of Dodge. To travel as quickly as possible, each alternates walking and riding their only horse, Sparky, as follows. Butch begins walking as Sundance rides. When Sundance reaches the first of their hitching posts that are conveniently located at one-mile intervals along their route, he ties Sparky to the post and begins walking. When Butch reaches Sparky, he rides until he passes Sundance, then leaves Sparky at the next hitching post and resumes walking, and they continue in this manner. Sparky, Butch, and Sundance walk at 6, 4, and 2.5 miles per hour, respectively. The first time Butch and Sundance meet at a milepost, they are n miles from Dodge, and have been traveling for t minutes. Find n + t.

5 Let B be the set of all binary integers that can be written using exactly 5 zeros and 8 ones where leading zeros are allowed. If all possible subtractions are performed in which one element of B is subtracted from another, find the number of times the answer 1 is obtained.

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