Henry Ernest Dudeney/Puzzles and Curious Problems/165 - The Postage-Stamps Puzzle/Solution

by : $165$

 * The Postage-Stamps Puzzle

Solution

 * $2519$.

Proof
Let $n$ be the number of stamps in the collection.

We have that $n + 1$ is divisible by $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$ and $10$.

The smallest such $n + 1$ is $\lcm \set {2, 3, 4, 5, 6, 7, 8, 9, 10}$ which is $8 \times 9 \times 5 \times 7 = 2520$.

No other number smaller than $3000$ fits the conditions.

Hence $n = 2519$.