How many eggs are there in the basket?

Question

There is a basket of eggs. The remainder is

• $1$ when we put the eggs in groups of $2$.
• $2$ when we put the eggs in groups of $3$.
• $3$ when we put the eggs in groups of $4$.
• $4$ and $5$, respectively, when we put the eggs in groups of $5$ and $6$.

How many eggs are there in the basket?

Answer 1

Hint. If you have $n$ eggs, then $n+1$ is divisible by $2$, $3$, $4$, $5$, and $6$.