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Mathtime Version 1 Edition 1

Mathtime Magazine Volume 1 Edition 1 is here

Number Theory

Problem 1

What is the last digit of the product of all odd integers between $1$ and $1,000?$

Problem 2

What is the $2011$th letter in the sequence $\text{MATHLETEMATHLETEMATHLETE}\ldots?$

(Inspiration of Problem: Alcumus/AMC 8)

Problem 3

What is $\dfrac{4042110}{4038090}?$

Problem 4

What is the sum of the digits of the square root of $9801?$

Problem 5

Find the sum of the digits of $35435_{7}+13362_{7}$ in base $7$.

Problem 6

Find $111_{2}+222_{4}+444_{8}$ in binary form.

Problem 7

Find the difference between $444_{8}$ and $222_{4}$ in base 8.

Problem 8

In what base is $66+87+85+48$ equal to $132?$

Problem 9

Find the value of $324_{5}+18_{10}$ in base ten.

Problem 10

What is $0_{4}$, $1_{4}$, $2_{4}$, $3_{4}$, and $1230_{4}$ in binary form?

Problem 11 $n\equiv0\pmod{3}$, $n\equiv0\pmod{7}$, and $n\equiv1\pmod{8}$. What is the smallest positive integer that satisfies the above?