This is a well known children's musical piece, the vowels have been removed and the remaining letters have been grouped together. Can you determine the correct words?
lttl mssm ffts tntf fttn ghrc rdsn dwhy thrc mbgs pdrw hstd wnbs dhrn dfrg htnd mssm fftw y
Reasoning
By likely, we mean greater than 50% chance.
With one person there is a 0 percent chance that you'll have two people with the same birthday.
With two people the probability that they won't share a birthday is 364 ÷ 365. The probability that they will share a birthday is therefore 1 − (364 ÷ 365).
With three people the probability that they won't share a birthday is the same as for two people, times 363 ÷ 365. So the probability that three people will share a birthday is 1 − (364 ÷ 365) x (363 ÷ 365).
Notice that with each additional person added, the probability that they shares a birthday with one of the previous persons goes up, because there are fewer "free" days remaining.
We keep adding people until the %age is greater than 50%.
When we have 23 people the %age is 50.729%.
??
Puzzle 3
What is the smallest positive integer, which, when multiplied by 6 …