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 Sum Digit Concern (Posted on 2010-03-13)
For a positive integer P drawn at random between 2 (base ten) and 2001 (base ten) inclusively, determine the probability that the sum of the digits in the base-P representation of 2009 (base ten) is equal to 11 (base ten).

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

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 Computer Solution | Comment 1 of 2

LASTYEAR = 2009

FOR p = 2 TO 2001

total = total + 1

baseP\$ = Base\$(LASTYEAR, p)
digitSum = SumDigits(baseP\$)

IF digitSum = 11 THEN
count = count + 1
PRINT p, baseP\$
END IF

NEXT p

PRINT
PRINT count, total, count/total

END

This code produced the following output:

4             133121
7             5600
10            2009
223           92
334           65
667           38
1000          29
1999          1A

8             2000          0.004

Therefore the probability is 0.4% (if we allow A to represent 10 for base 1999).

 Posted by Jim Keneipp on 2010-03-13 12:54:28

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