A.1153. In the last half an hour of an evening TV program there will be a poem recital, a ballet performance, a folk dance performance, and a story-teller. In how many different orders can the director put these performers if the two dance performances cannot follow one another?
A.1154. There are 4 boys and 5 girls in the Polka dots folk dance company. After two and a half minutes of group dance every boy dances a half-minute pair-dance with every girl. How long is the company’s performance?
A.1155. There are 156 seats in the school’s theater. On the first performance of the latest musical a third of the seats were taken, on the second performance a quarter of the seats were empty, and on the third performance only 28 seats were empty. On the final performance there were so many people that a third of them had to be standing because all the seats were taken. How many tickets were sold for the 4 performances if every spectator bought a ticket?
A.1156. On the school’s Talent Show each of the four judges used a 1 – 10 scale to evaluate the performances. For her singing, Melissa received a different score from every judge. If you add any two of these scores, you get the following sums: 11, 12, 14, 15, 17, and 18. What is the total number of points Melissa received from the judges?
A.1157. There are four instruments in a string quartet: violin, viola, cello, and bass. In the piece they played not all four instruments were used all the time. Sometimes only one, two or three instruments played at the same time, but of course, many times all four of them made music together. In how many different arrangements could we hear the instruments playing?
A.1158. In a fourth grade class many of the 23 students participated in the Talent Show. 10 of them danced, 9 of them sang, and 7 of them played an instrument. Three students danced and also played an instrument. Five students played an instrument and also sang, while six students sang and also danced. Only two students showed all three of these talents. How many students showed only one of their talents? How many students did not participate in the Talent Show at all from this class?
A.1159. In a pet store there is a huge, 3-story bird cage. 21 birds live above and 24 birds live below other birds in this cage. Just as many birds live on the middle level as on the bottom and on the top put together. How many birds live on each level?
A.1160. Two painted turtles, Ann and Bella, are 5 meters apart. They start crawling towards each other at the same time. Ann can crawl 70 cm in 2 minutes, and Bella can crawl 20 cm in one minute. How far will they be from each other 8 minutes later?
Please send your solutions here.
The Sharma Kamala Educational Trust is sponsoring the participation of students from India. So, if you are a student living in India, please, send your solutions to: Group A from India
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