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

Puzzles and Curious Problems by Henry Ernest Dudeney: $165$

The Postage-Stamps Puzzle

A youth who collects postage stamps was asked how many he had in his collection, and he replied:

"The number, if divided by $2$, will give a remainder $1$;

divided by $3$, a remainder $2$;

divided by $4$, a remainder $3$;

divided by $5$, a remainder $4$;

divided by $6$, a remainder $5$;

divided by $7$, a remainder $6$;

divided by $8$, a remainder $7$;

divided by $9$, a remainder $8$;

divided by $10$, a remainder $9$.

But there are fewer than $3000$."

Can you tell how many stamps there were in the album?

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $165$. -- The Postage-Stamps Puzzle
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $232$. The Postage Stamps Puzzle