In a certain multiplication sample all the digits were replaced by their mod 3 value (e.g. 875 became 212),rendering:
1202*102=222210
Please restore the original sample and either show that there are no others or provide extra solutions.

DEFDBL A-Z
OPEN "mod 3 alphametics.txt" FOR OUTPUT AS #2
FOR a = 1 TO 9 STEP 3
    FOR b = 2 TO 9 STEP 3
        FOR c = 0 TO 9 STEP 3
            FOR d = 2 TO 9 STEP 3
                FOR e = 1 TO 9 STEP 3
                    FOR f = 0 TO 9 STEP 3
                        FOR g = 2 TO 9 STEP 3
                            m1 = 1000 * a + 100 * b + 10 * c + d
                            m2 = 100 * e + 10 * f + g
                            prod = m1 * m2
                            prods$ = LTRIM$(STR$(prod))
                            IF LEN(prods$) = 6 THEN
                                good = 1
                                FOR i = 1 TO 6
                                    v1 = VAL(MID$(prods$, i, 1)) MOD 3
                                    v2 = VAL(MID$("222210", i, 1))
                                    IF v1 <> v2 THEN good = 0
                                NEXT
                                IF good THEN
                                    PRINT m1; m2, prod
                                    PRINT #2, m1; m2, prod
                                END IF
                            END IF
                        NEXT
                    NEXT
                NEXT
            NEXT
        NEXT
    NEXT
NEXT
CLOSE

finds

 1202  435     522870
 1268  462     585816
 1292  198     255816
 1505  168     252840
 1598  162     258876
 1832  138     252816
 1898  465     882570
 4232  195     825240
 4265  138     588570
 4298  192     825216
 4595  192     882240
 4598  192     882816
 7862  105     825510

Posted by Charlie on 2014-04-15 16:21:51