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 Point to 2013 (Posted on 2013-01-09)
Determine the minimum value of a positive integer N such that the 2nd, 3rd, 4th and 5th digits in order immediately following the decimal point (reading left to right) in the base ten expansion of √N is 2013.

*** For an extra challenge, solve this puzzle without using a computer program.

 No Solution Yet Submitted by K Sengupta No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: No Subject Comment 7 of 7 |
(In reply to No Subject by brianjn)

DEFDBL A-Z
CLS

found = 0
FOR i = 1 TO 999
FOR j = 0 TO 9
low = i + j / 10 + .02013#: high = i + j / 10 + .02014#
low2 = low * low: high2 = high * high
IF INT(high2) <> INT(low2) THEN
PRINT INT(high2), SQR(INT(high2))
found = found + 1
END IF
NEXT j
IF found > 20 THEN EXIT FOR
NEXT
PRINT

finds

`4532          67.3201307188273413976         118.220133649053222207         149.020132868012223019         151.720137094586131620         177.820133843161942568         206.320139588940757322         239.420132820947269127         262.920139966492588816         298.020133548054196547         310.7201313079022100375        316.8201382488178116636        341.5201311782367121536        348.6201371120148137137        370.3201317778983147011        383.4201350998667149862        387.1201363917925165584        406.9201395851525169102        411.2201356937668186555        431.9201315058144197776        444.7201367152155199827        447.0201337747552`

differing from brian's list by including 22207 and 88816, and does not include 56664 (my list has 21, yours 20). You will see from the former listing that sqrt(56664) is in fact  238.0420130985285, where the "2013" doesn't start until the 3rd place after the decimal point. The two included in my list but not yours both have a zero immediately after the decimal point and are the only two such.

I think it was better to start with the desired square root and square it rather than parse the square root of every integer.

Edited on January 10, 2013, 11:57 am
 Posted by Charlie on 2013-01-10 11:49:58

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