All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Some digits sum square (Posted on 2011-06-22)
Determine the probability that for a positive integer N drawn at random between 2 and 201 inclusively, the sum of the digits in the base N representation of 2011 (base ten) is a perfect square.

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

Comments: ( Back to comment list | You must be logged in to post comments.)
 computer solution | Comment 1 of 2

19 out of the 200 numbers in this range satisfy the condition, for a probability of 19/200 = 0.095, or about 1/10.5263157894736842104.

` N(base)  sod     base-10 representation of the base-N digits 2       9       1  1  1  1  1  0  1  1  0  1  1 3       9       2  2  0  2  1  1  1 8       16      3  7  3  3 10      4       2  0  1  1 20      16      5  0  11 22      16      4  3  9 26      36      2  25  9 60      64      33  31 80      36      25  11 92      100     21  79 106     121     18  103 110     49      18  31 127     121     15  106 134     16      15  1 136     121     14  107 148     100     13  87 178     64      11  53 190     121     10  111 194     81      10  71 stats: 19      200     19//200         0.095   10.5263157894736842104 list    5   dim Dig(20)   10     for N=2 to 201   20       Sod=0:NumDigs=0   30       Num=2011   40       while Num>0   50         D=Num @ N:inc NumDigs:Dig(NumDigs)=D   60         Sod=Sod+D   70         Num=Num\N   80       wend   90       Sr=int(sqrt(Sod)+0.5)  100       if Sr*Sr=Sod then inc Psqrs  101         :print N,Sod,  102         :for I=NumDigs to 1 step -1  103           :print Dig(I);  104         :next:print  110       inc NCt  120     next N  130     print Psqrs,NCt,Psqrs//NCt,Psqrs/NCt,NCt/PsqrsOK`

 Posted by Charlie on 2011-06-22 13:51:00

 Search: Search body:
Forums (0)