Determine the number of ordered solutions for integers such that they satisfy the equation above.
How many 6-digit numbers can be formed using exactly 4 different digits?
We want to create a divisible sequence of length starting from a number . In a Divisible Sequence, every term (except the starting number) is a divisor of the previous term. Examples of divisible sequences of length 3 starting with 10 are:
... etc.
Find the number of divisible sequences of length 5 starting from the number 360.
Seven identical eggs are being put into a egg box. However no more than two eggs can be put in a row. For example, one possible arrangement is E-E----EE-E--EE.
How many possible arrangements are there for the eggs?
Note: The egg box always stays in the same orientation so reflections count.
Let be the number of partitions of . Let be the number of partitions of into exactly parts. For example, because Compute
Definition: A partition of an integer is an expression of the integer as a sum of one or more positive integers, called parts. Two expressions consisting of the same parts written in a different order are considered the same partition ("order does not matter").