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Point to 2012 (Posted on 2012-04-04) Difficulty: 3 of 5
Determine the minimum value of a positive integer N such that the four digits immediately following the decimal point in the base ten expansion of √N is 2012.

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

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

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re(2): computer solution | Comment 5 of 7 |
(In reply to re: computer solution by Ady TZIDON)

The integer parts of the square roots do seem to come in grouped arithmetic progressions with a difference of 5 in each case, with an increasing number of members the higher you go:

 3869             62.2012861603359452591
 19377           139.2012930974421659664
 20794           144.2012482608940524978
 22261           149.201206429438766787
 46743           216.2012950932533151369
 48930           221.2012658191629788576
 51167           226.2012378392302255528
 53454           231.2012110694924539023
 85967           293.2012960407917432914
 88924           298.2012743098191389752
 91931           303.2012532955627477446
 94988           308.2012329631404962592
 98095           313.2012132798977520588
 137049          370.2012965941637541524
 140776          375.2012793155161937766
 144553          380.2012624913284003757
 148380          385.2012461039034593221
 152257          390.2012301364515175687
 156184          395.2012145730324042876
 199989          447.2012969569743991575
 204486          452.2012826164914804685
 209033          457.201268589666098271
 213630          462.201254866319029123
 218277          467.2012414367068010519
 222974          472.2012282914986234587
 227721          477.2012154217547673491
 232518          482.2012028189062906248
 274787          524.2012972131984337254
 280054          529.2012849568678059786
 285371          534.2012729299697204157
 290738          539.2012611261216254685
 296155          544.2012495391755345909
 301622          549.2012381632073487544
 307139          554.2012269925067569364
 312706          559.2012160215676784217
 318323          564.2012052450792133099
 361443          601.2012974037897067585
 367480          606.2012867026925075726
 373567          611.2012761766781520665
 379704          616.2012658214846607992
 385891          621.2012556329872712502
 392128          626.201245607192959694
 398415          631.2012357402352234403
 404752          636.2012260283691091151

  Posted by Charlie on 2012-04-04 14:49:42
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