## State Competitions

*State Competitions are coming up fast! Are you ready to compete? Let’s try a few 2019 State Competition problems to get ready. *

__2019 State Sprint Round, #18__

If C is a digit such that the product of the three-digit numbers 2C8 and 3C1 is the five-digit number 90C58, what is the value of C?

__2019 State Target Round, #7__

Andy has a cube of edge length 10 cm. He paints the outside of the cube red and then divides the cube into smaller cubes, each of edge length 1 cm. Andy randomly chooses one of the unit cubes and rolls it on a table. If the cube lands so that an unpainted face is on the bottom, touching the table, what is the probability that the entire cube is unpainted? Express your answer as a common fraction.

__2019 State Team Round, #4__

Suppose that Martians have eight fingers and use a base-eight (octal) number system. If Marty the Martian says he is 37 years old on Mars, how old is he in Earth’s base-ten system?

__2019 State Countdown Round, #12__

For a particular sequence, each term is the sum of the three preceding terms. If *a*, *b*, *c*, *d*, *e*, 0, 1, 2, 3 are consecutive terms of this sequence, what is the value of *a* + *b* + *c* + *d* + *e*?

**CHECK THE ****PROBLEM OF THE WEEK ARCHIVE****FOR SOLUTIONS TO PREVIOUS PROBLEMS**

#### It’s Not Too Late to Win E-Week Prizes!

Because many schools were closed last week for winter breaks, MATHCOUNTS has decided to extend the deadline for prizes and recognition through **Friday, 2/28**! Solve as many of our E-Week Problems of the Day as you can and then submit your answers in our webform to be entered to win great prizes and to be recognized on our Future Engineers page. Individuals, math classes, math teams, math clubs and other groups all can play!