MathGoldMedalist

Sign In Register

← Back to Problems

AMC 12A 2023 (Problem 24)

Let

K

be the number of sequences

A_1,A_2,\ldots,A_n

such that

n

is a positive integer less than or equal to

10

, each

A_i

is a subset of

\{1,2,3,\ldots,10\}

, and

A_{i-1}

is a subset of

A_i

for each

i

between

2

and

n

, inclusive. For example,

\{\},\{5,7\},\{2,5,7\},\{2,5,7\},\{2,5,6,7,9\}

is one such sequence, with

n=5

. What is the remainder when

K

is divided by

10

?

\text{(A)}\;1

\text{(B)}\;3

\text{(C)}\;5

\text{(D)}\;7

\text{(E)}\;9