perplexus.info :: Numbers : Find Fifty

Find Fifty (Posted on 2010-11-06)

(I) N is a duodecimal (base 12) 50 digit positive integer of the form XX....Y, where X is repeated precisely 49 times followed by Y, such that N is divisible by the duodecimal number 137. Each of X and Y is a different duodecimal digit from 1 to B.

Determine the possible value(s) of N.

(II) P is a duodecimal (base 12) 50 digit positive integer of the form XX....Y, where X is repeated precisely 49 times followed by Y, such that P is divisible by the duodecimal number 147. Each of X and Y is a different duodecimal digit from 1 to B.

Determine the possible value(s) of P.

Submitted by K Sengupta

Rating: 4.0000 (2 votes)

Solution: (Hide)

(I) N consists of 49 duodecimal 5's and an 8.
(II) P consists of 49 duodecimal 9's and a 5.
The decimal (base 10) values of N and P are respectively:
413656279545552262423981148879207560223961481966208468 and 744581303181994072363166067982573608403130667539175233
For an explanation, refer to the computer program assisted solution submitted by Charlie in this location and the analytical solution submitted by broll in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
posible analytical solution	broll	2010-11-07 06:10:43
re: solution	Charlie	2010-11-06 18:34:54
solution	Charlie	2010-11-06 18:31:52

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