You are almost certainly wrong about that
. My spreadsheet shows Trump with the thinnest of a chance of getting to a majority on the first ballot even giving him all of New York and New Jersey. Cruz, even less, but Cruz has a better than even chance of more pledged delegates than Trump. Trump and Cruz ought to have the horsepower between them to make sure that a third party can't slip in. They ought to reach an agreement that whoever has the greatest number of votes on the first ballot is elected on the second, either Trump or Cruz.
No. The way it works is that last person who has not been mathematically eliminated from 1237 delegates is the nominee.
That is Trump.