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.
(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
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Posted by Charlie
on 2012-04-04 14:49:42 |
re(2): computer solution
