TWO+TWO=NULL
TWO+TWO=ONE
TWO+TWO=FOUR
TWO+TWO=FIVE
TWO+TWO=SIX
TWO+TWO=NINE
Each one of the above mentioned alphametics, treated separately, has more than one base ten solution. Which one has the most? Which one of them, if any, possess an unique solution in another base or bases?

(In reply to Only Base 10 by brianjn)

Charlie posted at the same time as me but reached the server first.

I note that for our base 10 values we are in agreement with just one value, that for NULL at 4.

             NULL  ONE  FOUR   FIVE  SIX  NINE
Charlie     4      12      6        15     42     3
brianjn     4      17      7        35     64    11

To arrive at each of my tallies (and the value sets in my prior comment) I used QuickBASIC and a program listing emulating a format that Charlie frequent uses on Perplexus.

I have taken my list (from prior comment) into Excel to check that the first column is in fact half that of the second.  Cursory inspection of my values seems that except where a specific letter is duplicated all other values for the Two and the Total are unique.

I shall not present all listings but this is tha one I used for SIX.


OPEN "six.txt" FOR OUTPUT AS #1
count = 0
CLS
FOR t = 1 TO 9
IF used(t) = 0 THEN
used(t) = 1
FOR w = 0 TO 9
IF used(w) = 0 THEN
used(w) = 1
FOR o = 1 TO 9
IF used(o) = 0 THEN
used(o) = 1
FOR s = 1 TO 9
IF used(s) = 0 THEN
used(s) = 1
FOR i = 0 TO 9
IF used(i) = 0 THEN
used(i) = 1
FOR x = 0 TO 9
IF used(x) = 0 THEN
used(x) = 1
two = t * 100 + w * 10 + o
six = s * 100 + i * 10 + x
IF six = 2 * two THEN
 count = count + 1
 PRINT #1, two; six; count
 PRINT two; six; count
END IF
used(x) = 0
END IF
NEXT
used(i) = 0
END IF
NEXT
used(s) = 0
END IF
NEXT
used(o) = 0
END IF
NEXT
used(w) = 0
END IF
NEXT

used(t) = 0
END IF
NEXT


CLOSE 1

Posted by brianjn on 2010-04-11 23:06:51