MathDB

Teresa the bunny has a fair

8

-sided die. Seven of its sides have fixed labels

1, 2, \cdots , 7,

and the label on the eighth side can be changed and begins as

1

. She rolls it several times, until each of

1, 2, \dots, 7

appears at least once. After each roll, if

k

is the smallest positive integer that she has not rolled so far, she relabels the eighth side with

k

. The probability that

7

is the last number she rolls is

\tfrac ab,

where

a

and

b

are relatively prime positive integers. Compute

100a + b

Problem Statement