英数第三周周三,1.I have 6 different books, 3 with red covers and 3 with blue covers. In how many different ways can I arrange these books on a shelf so that no two books of the same colour are next to each other?,2. Assume that a ball dropped from any height rises half the distance on the rebound.If a ball is dropped from 100m, what distance will the ball have covered by the time it hits the ground the 4th time?,3. How many 3 letter ”words” can be made using the consonants B C D,and the vowels A and E? A “word” is definded to be any sequence of 3 letters containing two consonants and one vowel in any order (allowing letters to be repeated). For example,ABC and CCE are both “words”.,4. A set of 1*1*1 cubes is used to construct a hollow 10*10*10 cube whose shell is two layers of cubes in thickness. How many cubes are needed?,5. What is the next number in the sequence 1,2,3,4,6,9,13,19,28,.?,6. The prime numbers between 10 and 20 are added together to form the number Q. What is the largest prime divisor of Q?,7. Jim drives 60 km south,40 km west , 20 km north, and 10 km east. What is the distance from his starting point to his finishing point?,8. In how many different ways can seven numbers be closen from the numbers 1 to 9,inclusive, so that the seven numbers have a sum which is a multiple of 3?,9. An ant walks inside a 150cm by 18cm rectangle. The ants path follows straight lines which always make angles of 45to the sides of the rectangle.The ant starts from a point X on one of the shorter sides.The first time the ant reaches the opposite side,it arrives at the midpoint.What is the distance,in centimetres,from X to the nearest corner of the rectangle？,10. How many five-digit integers, divisible by 9, can be written using only the digits 3 and 6?,答案： 72 275m 54 784 41 5 50 km 12 3 10,