Let $n$ be the number of different $5$ digit numbers, divisible by $4$ with the digits $1, 2, 3, 4, 5$ and $6,$ no digit being repeated in the numbers. What is the value of $n?$

In some code, letters, $a, b, c, d$ and $e$ represent numbers $2, 4, 5, 6$ and $10.$ However, we don't know which letter represent which number. Consider the following re...

A set of consecutive positive integers beginning with $1$ is written on the blackboard. A student came along and erased one number. The average of the remaining numbers i...

All the page numbers from a book are added, beginning at page $1.$ However, one page number was mistakenly added twice. The sum obtained was $1000.$ Which page number was...

Every ten years the Indian government counts all the people living in the country. Suppose that the director of the census has reported the following data on two neighbou...

In a number system the product of $44$ and $11$ is $1034.$ The number $3111$ of this system, when converted to the decimal number system, becomes$406$$1086$$213$$691$