# E there is neither partial credit nor a penalty for

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i.e., there is neither partial credit nor a penalty for wrong answers. 3. No aids other than scratch paper, graph paper, ruler, compass, and pro- tractor are permitted. In particular, calculators and computers are not permitted. 4. A combination of the CIME and the Christmas Mathematics Contest 12 are not used to determine eligibility for participation in the Christmas Ju- nior Mathematical Olympiad (CJMO). A combination of the CIME and the Christmas Mathematics Contest 10 are not used to determine eligibility for participation in the Christmas Junior Mathematical Olympiad (CJMO). All students are eligible to participate in the Christmas Junior Mathematical Olympiad. The CJMO will be given from FRIDAY, January 4, 2019 to FRIDAY, January 25, 2019. 5. You may obtain an AIME answer form from - competitions/aime-archive , and record all of your answers, and certain other information, on the AIME answer form. The answer form will not be collected from you, only your submission on the AIME Submission Form found at . c Committee on the Christmas Mathematics Competitions
2019 CIME I Problems 3 8. In parallelogram ABCD, the circumcircle of BCD has center O and intersects lines AB and AD at E and F, respectively . Let P and Q be the midpoints of AO and BD, respectively . Suppose that PQ = 3 and the height from A to BD has length 7 . Find the value of BF · DE. 9. Let N denote the number of strictly increasing sequences of positive integers a 1 , a 2 , · · · , a 19 satisfying the following two rules: a 1 = 1 and a 19 = 361 , for any i = j, if b ij is the ( i · j ) th number not in the sequence , then ( a i - b ij )( a j - b ij ) < 0 .

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• Fall '19
• Natural number, Prime number, CIME, CJMO

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