A singer performed concert 3 times and sang ten songs in each concert.
Out of ten songs in each concert he sang five songs which he did not sing in other two concerts.
In case the same song sung even twice or more is counted as one song, how many songs the most did this singer sing in three concerts ?
Out of ten songs in each concert he sang five songs which he did not sing in other two concerts.
In case the same song sung even twice or more is counted as one song, how many songs the most did this singer sing in three concerts ?
Answer
Since he sang five songs which are not sung in other two concerts, at least 5 times × 3= 15 times are different songs.
While of 30 - 15 times = 15 times, the same song is sung at least 2 times respectively in each concert.
In order to have the most number of songs, songs sung three times should be less as much as possible.
When the number of the song sung 3 times is 0 time, it is useless since 15 times cannot be divisible by 2.
When the number of song sung 3 times is 1 time, 15 - 3 × 1 = 12. 12 can be divisible by 2 and it is 12/2 = 6.
Therefore, most numbers of song are 15 + 6 + 1 = 22 songs.
22 songs
Solution
The number of times of singing in three concerts is 10 times × 3= 30 times.
Since he sang five songs which are not sung in other two concerts, at least 5 times × 3= 15 times are different songs.
While of 30 - 15 times = 15 times, the same song is sung at least 2 times respectively in each concert.
In order to have the most number of songs, songs sung three times should be less as much as possible.
When the number of the song sung 3 times is 0 time, it is useless since 15 times cannot be divisible by 2.
When the number of song sung 3 times is 1 time, 15 - 3 × 1 = 12. 12 can be divisible by 2 and it is 12/2 = 6.
Therefore, most numbers of song are 15 + 6 + 1 = 22 songs.
