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 From Poland with love (Posted on 2012-12-13)
On my boring (No food, no TV) flight from Krakow to Paris I have created, solved and debugged the following alphametics:

Apparently there are 2 possible solutions.
a. (D2) Find both.

b. (D4) What is the maximum value of POLSKA + KRAKOW if the digits corresponding to the word POLSKA form a square number?

Rem : Each letter corresponds to a certain digit (distinct in each case) - other than that there are no restrictions.

 No Solution Yet Submitted by Ady TZIDON No Rating

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 computer solution | Comment 1 of 2

DECLARE SUB permute (a\$)

CLS

a\$ = "1234567890": h\$ = a\$
DO
p = VAL(MID\$(a\$, 1, 1))
o = VAL(MID\$(a\$, 2, 1))
l = VAL(MID\$(a\$, 3, 1))
s = VAL(MID\$(a\$, 4, 1))
k = VAL(MID\$(a\$, 5, 1))
a = VAL(MID\$(a\$, 6, 1))
r = VAL(MID\$(a\$, 7, 1))
w = VAL(MID\$(a\$, 8, 1))
n = VAL(MID\$(a\$, 9, 1))
e = VAL(MID\$(a\$, 10, 1))
polska = VAL(LEFT\$(a\$, 6))
krakow = 100100 * k + 10000 * r + 1000 * a + 10 * o + w
answer = 100000 * a + 10000 * n + 1000 * s + 100 * w + 10 * e + r
permute a\$
LOOP UNTIL a\$ = h\$
PRINT "paused"
PRINT : PRINT

DO: LOOP UNTIL INKEY\$ > ""
part2:

a\$ = "1234567890": h\$ = a\$
DO
p = VAL(MID\$(a\$, 1, 1))
o = VAL(MID\$(a\$, 2, 1))
l = VAL(MID\$(a\$, 3, 1))
s = VAL(MID\$(a\$, 4, 1))
k = VAL(MID\$(a\$, 5, 1))
a = VAL(MID\$(a\$, 6, 1))
r = VAL(MID\$(a\$, 7, 1))
w = VAL(MID\$(a\$, 8, 1))
n = VAL(MID\$(a\$, 9, 1))
e = VAL(MID\$(a\$, 10, 1))
polska = VAL(LEFT\$(a\$, 6))
sr = INT(SQR(polska) + .5)
IF sr * sr = polska THEN
krakow = 100100 * k + 10000 * r + 1000 * a + 10 * o + w
sum = polska + krakow
IF sum >= max THEN
PRINT polska, krakow, sum
max = sum
END IF
END IF
permute a\$
LOOP UNTIL a\$ = h\$

finds

`polska  krakow  answer489516  136187  625703675318  128174  803492`

and the final, largest line for part b is

`polska        krakow760384   +    894865   =    1655249`

 Posted by Charlie on 2012-12-13 15:48:57

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