In a certain class of 40 students, three class representatives will be decided by an election.
All 40 students voted someone of this class by one vote per person.
As a result, Taro was in the 1st place, Jiro was in the 2nd place and Hanako was in the 3rd place.
The number of votes of three persons was different and there is no student who got same number of votes as Hanako in other 37 persons. Answer the following questions.
(1) Find the most number of votes which Taro gained among possible number of votes.
Moreover, also find the smallest number of votes.
(2) How many ways of number of votes which Hanako gained among possible number of votes?
(3) The sum total of the number of votes which three persons, Taro, Jiro, and Hanako, gained was 37 votes.
Moreover, the difference of the number of votes Jiro and Hanako gained was twice the difference of the number of votes Taro and Jiro gained.
In this case, find the number of votes Taro gained.
Find all numbers of votes possibly gained.