Counting Problems( Week 8 Evaluation) 1. There are 20 triangles. Each triangle has exact one shared side with another triangle. How many sides are there in total? 2. A book has 400 pages numbered 1, 2, 3, ... and so on. In how many pages does the digit 5 appear more than once in the page number? 4. A 12-hour chime clock strikes 1 chime at 1 o'clock, 2 chimes at 2 o'clock, 3 chimes at 3 o'clock,..., and 12 chimes at 12 o'clock. The clock also strikes 1 chime in the middle of every hour. What is the maximum total number of chimes the clock will strike in a 470-minutes period? 5. A 12-hour chime clock strikes 1 chime at one o'clock, 2 chimes at two o'clock, 3 chimes at three o'clock,..., and 12 chimes at 12 o'clock. What is the maximum total number of chimes the clock will strike in a hours period? 6. A is the sum of the odd numbers from 1 through 107, and B is the sum of the even numbers from 2 through 108. What is the difference between A and B? 7. How many whole numbers are there between 50 and 690 that have a 5 or 9 in their ones digit? 8. When a natural number is multiplied by itself, the result is a square number. Such as 1, 4, 9, 16, and 25. How many square numbers are there between 6000 and 7000 inclusively? 9. A book has 100 pages numbered 1, 2, 3, ..., and so on. In how many pages does the digit 1 appear in the page numbers? 10. A book has 500 pages numbered 1, 2, 3,...and so on. How many times does the digit 1 appear in the page numbers? |