## 2018 National Champion

Last week the National Competition concluded, and Luke Robitaille from Texas became the first ever two-time MATHCOUNTS National Champion. Let’s look at some of the problems he had to solve on the way to the top!

In a card game, Nora draws cards at random, without replacement, from a deck of 21 cards. Twenty of the cards are numbered 1 through 20, and the other card is marked “Joker.” Nora keeps all of the cards she draws before she draws the Joker. What is the probability that the cards Nora keeps include exactly four prime-numbered cards? Express your answer as a common fraction.

*[Sprint #17] *

A *4-up number *is defined as a positive integer that is divisible by neither 2 nor 3 and does not have 2 or 3 as any of its digits. How many numbers from 400 to 600, inclusive, are 4-up numbers?

*[Target #7] *

Captain Greenbeard’s treasure chest holds 100 grams of a mix of gold, silver and bronze coins. The gold, silver and bronze coins each weigh 6 grams, 2 grams and 5 grams, respectively, and are worth 30 droubles, 8 droubles and 15 droubles, respectively. Greenbeard has at least one of each kind of coin. What is the greatest possible total value, in droubles, of the coins in the chest?

*[Team #3] *

**♦ CHECK THE PROBLEM OF THE WEEK ARCHIVE FOR**

SOLUTIONS TO PREVIOUS PROBLEMS ♦