Why is a company offering to buy back their stock higher than value?

[flytrap]

First off, I have some investements, but I'm pretty much a novice when it comes to the ins and outs of investing. I recieved information from a company informing me they are willing to purchase for cash, shares of their stock at between $39 and $42. The stock is currently around $33, so I have a few questions.

First off, how do I know which price I will be getting, if I accept the offer?
Second, why wouldn't the company just buy shares the way everyone else does, and pay $33 a share, rather than offering shareholders a higher price? What's the part I'm missing?
Third, why wouldn't I just sell to them, then take that money and rebuy the stock on Ameritrade for the price it is listed at, which as I've said is lower than the companies offer? Thanks in advance.