Henry Ernest Dudeney/Puzzles and Curious Problems/151 - The Arithmetical Cabby

Puzzles and Curious Problems by Henry Ernest Dudeney: $151$

The Arithmetical Cabby

The driver of the taxi-cab was wanting in civility, so Mr. Wilkins asked him for his number.

"You want my number, do you?" said the driver.

"Well, work it out for yourself.

If you divide by number by $2$, $3$, $4$, $5$, or $6$ you will find there is always $1$ over;

but if you divide it by $11$ there ain't no remainder.

What's more, there's no other driver with a lower number who can say the same."

What was the fellow's number?

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $151$. -- The Arithmetical Cabby
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $223$. The Arithmetical Cabby