Number Bases: Level 3 Challenges Practice Problems Online

There is a number $a$ , which can be written as $\overline{xyz}$ in base 9 and $\overline{zyx}$ in base 6, for some positive integer $x,y,z$ . Find $x+y+z$ .

Details and Assumption

$\overline{xyz}$ represents reading the digits together, instead of multiplying them out. For example, $\overline{xyz}_9 = 81 x + 9y + z$ and $\overline{zyx}_6 = 36 z + 6y + x$ .

Find the smallest natural number greater than 3 which has the unit digit of 3 when expressed in base-4, base-5, base-6, base-7, and base-8.

Express your answer in base 10.

$N$ is an integer whose representation in base $b$ is 777. Find the smallest positive integer $b$ for which $N$ is the fourth power of an integer.

$(2^3)! = 40320_{10} = 1001\:1101\:1000\:0000_2.$

The factorial shown above has seven trailing zeros.

How many trailing zeroes does the number $(2^{16})!$ have in binary notation?

$1,3,4,9,10,12,13,\ldots$

The above sequence consists of the powers of $3$ or the sum of distinct powers of $3$ , arranged in increasing order.

Find the $100^\text{th}$ term of the sequence.

Concept Quizzes

Challenge Quizzes

Number Bases: Level 3 Challenges

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.