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Point to 2013 (Posted on 2013-01-09) Difficulty: 3 of 5
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    
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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          67.32013071882734
13976         118.2201336490532
22207         149.0201328680122
23019         151.7201370945861
31620         177.8201338431619
42568         206.3201395889407
57322         239.4201328209472
69127         262.9201399664925
88816         298.0201335480541
96547         310.7201313079022
100375        316.8201382488178
116636        341.5201311782367
121536        348.6201371120148
137137        370.3201317778983
147011        383.4201350998667
149862        387.1201363917925
165584        406.9201395851525
169102        411.2201356937668
186555        431.9201315058144
197776        444.7201367152155
199827        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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