Curriculum · Counting & Probability · Casework & Complementary

Counting with Recursion

States, transitions, and the recurrences behind tiling and path problems.

Objectives

Define states and transitions
Set up recurrences
Compute by building up

The full interactive edition of this lesson ships in v1.5. The topic is live everywhere else — the problems below feed your Casework & Complementary mastery now.

Train the topic

●●●○○How many integers from

1

100

are divisible by

3

5

?AMC 8 style ●●●○○How many three-digit numbers have digits summing to

5

?AMC 10 style ●●●○○A fair coin is flipped

4

times. The probability of at least two heads is

\tfrac{m}{n}

in lowest terms. What is

m + n

?AIME style