There are properties that hold for any possible choice, without exception. This riddle invites you to find why a certain outcome is inevitable, whatever the starting point.
The consecutive numbers
Riddle statement
Choose three consecutive integers and multiply them.
Why is the result always divisible by 6?
Show solution
Solution
Answer: because between three consecutive integers there is always a multiple of 2 and a multiple of 3.
In any group of three consecutive numbers, one of them is even. That contributes a factor 2 to the product.
Also, in any group of three consecutive numbers, one of them is a multiple of 3. That contributes a factor 3 to the product.
Therefore, the product has factors 2 and 3. As:
$
2\cdot 3=6,
$
the product is always divisible by 6.