MathDB

BMT 2021 Guts Round p25

Source:

October 7, 2022

algebra

Problem Statement

For any

p, q \in N

, we can express

\frac{p}{q}

as the base

10

decimal

x_1x_2... x_{\ell}.x_{\ell+1}... x_a \overline{y_1y_2... y_b}

, with the digits

y_1, . . . y_b

repeating. In other words,

\frac{p}{q}

can be expressed with integer part

x_1x_2... x_{\ell}

and decimal part

0.x_{\ell+1}... x_a \overline{y_1y_2... y_b}

. Given that

\frac{p}{q}= \frac{(2021)^{2021}}{2021!}

, estimate the minimum value of

a

. If

E

is the exact answer to this question and

A

is your answer, your score is given by

\max \, \left(0, \left\lfloor 25 - \frac{1}{10}|E - A|\right\rfloor \right)

.

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