 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Units Digit Determination (Posted on 2015-01-07) N is a 9-digit duodecimal (base 12) palindrome such that:

The first two digits of N are not consecutive, and:
The sixth and seventh digits of N are not consecutive

What is the units digit of the sum of all possible values of N?

*** N is of course positive and does not contain any leading zero.

 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.) corrected computer summation Comment 3 of 3 | The program previously shown ensured that not only did the first two digits, as well as digits 6 and 7 (by checking digits 3 and 4 in the palindrome), need to be non-consecutive, it also made sure the members of each pair were not equal to each other.  This has been corrected in lines 30 and 60 of the below programs.  The new totals, in decimal and then in the digits of the respective bases, follow the run command in each.

The units digit in the respective bases remains 0, but the coincidental unit-digit zero in the decimal representation no longer takes place.

10   for A=1 to 11
20   for B=0 to 11
30    if abs(A-B)<>1 then
40      :for C=0 to 11
50      :for D=0 to 11
60      :if abs(C-D)<>1 then
70        :for E=0 to 11
80          :N=A*(12^8+1)
90          :N=N+B*(12^7+12)
100          :N=N+C*(12^6+12^2)
110          :N=N+D*(12^5+12^3)
120          :N=N+E*12^4
130          :Tot=Tot+N
140        :next
144       :endif
145      :next
146      :next
150   next B
160   next A
200   print Tot
300   N=Tot
305   S\$=" "
310   while N>0
320      D=N@12:N=N\12
330      S\$=str(D)+S\$
340   wend
360   print S\$

run
457090751915976
4 3 3 2 3 2 11 11 11 8 6 5 10 0
OK

10   for A=1 to 15
20   for B=0 to 15
30    if abs(A-B)<>1 then
40      :for C=0 to 15
50      :for D=0 to 15
60      :if abs(C-D)<>1 then
70        :for E=0 to 15
80          :N=A*(16^8+1)
90          :N=N+B*(16^7+16)
100          :N=N+C*(16^6+16^2)
110          :N=N+D*(16^5+16^3)
120          :N=N+E*16^4
130          :Tot=Tot+N
140        :next
144       :endif
145      :next
146      :next
150   next B
160   next A
200   print Tot
300   N=Tot
305   S\$=" "
310   while N>0
320      D=N@16:N=N\16
330      S\$=str(D)+S\$
340   wend
360   print S\$

run
27956539129767392
6 3 5 2 5 2 15 15 15 10 10 5 14 0
OK

 Posted by Charlie on 2015-01-08 07:59:42 Please log in:

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