## 28. How Many Favorites?

- "Here's a different kind of puzzle," said the Gryphon. "Once, the Queen of Hearts held a reception for thirty guests. She needed to distribute one hundred gingerbread cookies among the guests. Instead of cutting the cookies into pieces, the Queen preferred to give four cookies to each of her favorites, and three cookies to the rest of the guests.

How many favorites did the Queen of Hearts have?"
28. How many favorites? This problem, usually solved using algebra, is very simple if approached in the following way. First, let's distribute 3 pretzels to each of the 30 guests of the Queen. We will have 10 pretzels left. At this point, all non-favorites will have received all the pretzels they are entitled to, while each of the favorites still needs to receive 1 more pretzel.

Therefore, all the remaining pretzels are intended for the favorites—one pretzel each. This means there must be 10 favorites.

Verification. Each of the 10 favorites should receive 4 pretzels, which totals 40 pretzels for all the favorites. Each of the remaining 20 guests will receive 3 pretzels, which adds up to another 60 pretzels. \(40 + 60 = 100\). Therefore, our solution is correct.