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

by : $174$

 * 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?