HMMT 二月 2000 · GEN 赛 · 第 13 题

英文原题

Ho w man y p erm utations of 123456 ha v e exa tly one n um b er in the orre t pla e? 14. The author of this question w as b orn on April 24, 1977. What da y of the w eek w as that? 15. Whi h is greater: (3 5 ) (5 3 ) or (5 3 ) (3 5 ) ? 16. Jo e bik es x miles East at 20 mph to his friend's house. He then turns South and bik es x miles at 20 mph to the store. Then, Jo e turns East again and go es to his grandma's house at 14 mph. On this last leg, he has to arry our he b ough t for her at the store. Her house is 2 more miles from the store than Jo e's friend's house is from the store. Jo e sp ends a total of 1 hour on the bik e to get to his grandma's house. If Jo e then rides straigh t home in his grandma's heli opter at 78 mph, ho w man y min utes do es it tak e Jo e to get home from his grandma's house? 17. In ho w man y distin t w a ys an the letters of ST ANTON b e arranged? 18. Y ou use a lo k with four dials, ea h of whi h is set to a n um b er b et w een 0 and 9 (in lusiv e). Y ou an nev er remem b er y our o de, so normally y ou just lea v e the lo k with ea h dial one higher than the orre t v alue. Unfortunately , last nigh t someone hanged all the v alues to 5. All y ou remem b er ab out y our o de is that none of the digits are prime, 0, or 1, and that the a v erage v alue of the digits is 5. Ho w man y om binations will y ou ha v e to try? 19. Elev en pirates nd a treasure hest. When they split up the oins in it, they nd that there are 5 oins left. They thro w one pirate o v erb oard and split the oins again, only to nd that there are 3 oins left o v er. So, they thro w another pirate o v er and try again. This time, the oins split ev enly . What is the least n um b er of oins there ould ha v e b een? 20. Giv en: AC has length 5, semi ir le AB has radius 1, semi ir le B C has diameter 3. What p er en t of the the big ir le is shaded? A B C