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 Mod 3 alphametics (Posted on 2014-04-15)
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.

 No Solution Yet Submitted by Ady TZIDON No Rating

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 In Basic code Comment 2 of 2 |

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

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