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Question Number 115194 by 1549442205PVT last updated on 24/Sep/20

Find a three−digits number whose digits form a geometry progression ;if you known that after substract that number by 495 ,get a number written by the same digits as the number you are looking for but in the reverse order;if the digits of the number obtained after substraction(from left right)reduced by 1,1 and 2 respectively ,you obtain an arithmetic progression

$$\mathrm{Find}\:\mathrm{a}\:\mathrm{three}−\mathrm{digits}\:\mathrm{number}\:\mathrm{whose} \\ $$$$\mathrm{digits}\:\mathrm{form}\:\mathrm{a}\:\mathrm{geometry}\:\mathrm{progression} \\ $$$$;\mathrm{if}\:\mathrm{you}\:\mathrm{known}\:\mathrm{that}\:\mathrm{after}\:\mathrm{substract}\:\mathrm{that} \\ $$$$\mathrm{number}\:\mathrm{by}\:\mathrm{495}\:,\mathrm{get}\:\mathrm{a}\:\mathrm{number} \\ $$$$\mathrm{written}\:\mathrm{by}\:\mathrm{the}\:\mathrm{same}\:\mathrm{digits}\:\mathrm{as}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{you}\:\mathrm{are}\:\mathrm{looking}\:\mathrm{for}\:\mathrm{but}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{reverse}\:\mathrm{order};\mathrm{if}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{obtained}\:\mathrm{after} \\ $$$$\mathrm{substraction}\left(\mathrm{from}\:\mathrm{left}\:\mathrm{right}\right)\mathrm{reduced} \\ $$$$\mathrm{by}\:\mathrm{1},\mathrm{1}\:\mathrm{and}\:\mathrm{2}\:\mathrm{respectively}\:,\mathrm{you}\:\mathrm{obtain} \\ $$$$\mathrm{an}\:\mathrm{arithmetic}\:\mathrm{progression} \\ $$

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