Staffing Talk is offering an Amazon gift card for the first correct answer to this math problem.  Open only to staffers and recruiters.  Note: there is no 'trick' to the problem, it can be deduced using pure logic.

"We won the contract," exclaimed Janet, owner of Wobegon Temps, to her executive team members Jill and Jeff.

They had worked on the deal, the biggest staffing contract to come along in years, for months, and it was theirs!  

Jill and Jeff were anxious to know what date they would start placing temps.  "What date does it start?" they asked in unison.

Janet, being a math whiz and a bit of a tease, decided to make a game out of it to see if they could determine the date on their own.  She gave the month number to Jill and the day number to Jeff and also provided them each with a list of the possible dates:

Feb 13, 17, 25
March 14, 28
April 2, 14
May 2, 13, 17

"I don't know the date," said Jill.  "But I also know that Jeff doesn't know the date either."

"At first I didn't know the date," said Jeff.   "But now I know."

"Oh, well now I, too, know the date," said Jill.

What date did the contract start?