In the United States, only governments can run lotteries (typically state governments run them leading to the U.S. joke that Lotteries are "taxes on being bad at math" given the low odds of winning).
To be a lottery, the winner must be determined by a random drawling, the prize must be of some monitary value (including items and things that are super expensive to purchase outside of the contest) and must have some form of consideration. If a company runs a prize giveaway and meets all three criteria, it's an illegal lottery for purposes of the law. However, you must meet all three to be a lottery, so many promotial give-aways will include in the contest rules that line about "no purchase necessary" to get around the "Consideration" which is a profit incentive to consider a subset of people.
It's actually in the typical name for these promotions. It's a "give-away" meaning they are giving you the prize for free, not requiring you to purchase a ticket to be drawn. So anyone can write in and get a ticket of some kind to be considered, however, if you buy the product (a candy bar) they'll throw in for free a ticket... there's no change to the candy bare's purchase price, so no profit there, and if you're too poor for a candy bar, or don't like that candy bar, you can always write in and get a free ticket without a candy bar for free (and by the way, it's actually better odds to write in, since the limit to entries for write in is usually per individual letters and winning the bigger prizes is limited to household... if you send 20 cards with requests printed on computer paper, and it's five request per card, it's much more cost efficient than buying 100 candy bars... and the prize limit only hits if someone in your household wins (typically winning a big prize), not if your family of five all send in 20 letters.
Another way is to make the prize a skill contest. Suppose you're asked to design a new mascot with a prize of having that mascot on the ceral box and in a commercial... that's not really of monitary value or randomly selected (since someone is evaluating your work) so you could require a "proof of purchase" for entry. This also works if you're giving away an toy or other promotional item... anyone who buys four boxes will get the prize, since the prize isn't being rewarded at random... just to select people who buy a lot of product.
It should also be noted that any profit to the company makes the contest a lottery, which is why your church (a non-profit organization) can fund raise with raffled items and ask that you buy tickets. The church legally has to spend all the money it brings in above and beyond operating costs (staff pay, bills, maintenance, ect) so there's nothing the contest will do to improve the churches bottom line and more than likely the money will go to an improvement.
