Henry Ernest Dudeney/Puzzles and Curious Problems/174 - More Curious Multiplication

Puzzles and Curious Problems by Henry Ernest Dudeney: $174$

More Curious Multiplication

What number is it that, when multiplied by $18$, $27$, $36$, $45$, $54$, $63$, $72$, $81$ or $99$,

gives a product in which the first and last figures are the same as those in the multiplier,

but which when multiplied by $90$ gives a product in which the last two figures are the same as those in the multiplier?

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $174$. -- More Curious Multiplication
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $238$. More Curious Multiplication