(In reply to
re: computer result: 11 solutions and two almost-solutions by Ady TZIDON)
The original program did not allow the 3- and 4-digit sets (along with the 2-digit sets, where it legitimately applies) to contain leading zeros, but that, of course, should not have applied to the set that merely accounted for one digit being twice another. That resulted in those solutions not being shown, as the "remainder" set (neither prime nor square) was shown only in it's ascending order, to eliminate trivial permutations, just as the reversible squares and primes were shown only as the lower of the two values.
Only one non-asterisked solution was missed: the one Ady pointed out. One more asterisked pseudo-solution popped up also. I've left them in for the record. It's easier to pick these out by hand than to program them out. Disregard them, and now we have an even dozen legitimate solutions.
The fixed version of the program:
DECLARE SUB permute (a$)
DATA 2,3,5,7,13,17,37,79,107,149,157,167
DATA 179,347,359,389,709,739,769,1069,1097,1237
DATA 1249,1259,1279,1283,1409,1429,1439,1453,1487
DATA 1523,1583,1597,1657,1723,1753,1789,1847,1867
DATA 1879,3019,3049,3067,3089,3109,3169,3257,3407
DATA 3467,3469,3527,3697,3719,3917,7219,7349,7459
DATA 7529,7589,7649
DIM rprime(61)
FOR i = 1 TO 61: READ rprime(i): NEXT
primct = 61
DIM rsquare(6)
WHILE sq < 10000
sq = n * n
sqs$ = LTRIM$(STR$(sq))
revs$ = "": good = 1: REDIM dig(9)
FOR i = 1 TO LEN(sqs$)
revs$ = MID$(sqs$, i, 1) + revs$
d = VAL(MID$(sqs$, i, 1))
IF dig(d) THEN good = 0
dig(d) = 1
NEXT
r = VAL(revs$)
sr = INT(SQR(r) + .5)
IF sr * sr = r AND r >= sq AND good = 1 THEN
sqct = sqct + 1
rsquare(sqct) = sq
PRINT sq;
END IF
n = n + 1
WEND
PRINT sqct
digs$ = "0123456789": h$ = digs$
OPEN "rprimesol2.txt" FOR OUTPUT AS #2
DO
IF MID$(digs$, 2, 1) > "0" THEN
hadprime = 0: hadsq = 0: haddouble = 0
a = VAL(MID$(digs$, 1, 1))
b = VAL(MID$(digs$, 2, 2))
c = VAL(MID$(digs$, 4, 3))
d = VAL(MID$(digs$, 7, 4))
FOR i = 1 TO primct
IF a = rprime(i) OR b = rprime(i) OR c = rprime(i) AND c > 99 OR d = rprime(i) AND d > 999 THEN
hadprime = hadprime + 1
IF a = rprime(i) THEN hp(hadprime) = 1
IF b = rprime(i) THEN hp(hadprime) = 2
IF c = rprime(i) AND c > 99 THEN hp(hadprime) = 3
IF d = rprime(i) AND d > 999 THEN hp(hadprime) = 4
END IF
NEXT
FOR i = 1 TO sqct
IF a = rsquare(i) OR b = rsquare(i) OR c = rsquare(i) AND c > 99 OR d = rsquare(i) AND d > 999 THEN
hadsq = hadsq + 1
IF a = rsquare(i) THEN hs(hadsq) = 1
IF b = rsquare(i) THEN hs(hadsq) = 2
IF c = rsquare(i) AND c > 99 THEN hs(hadsq) = 3
IF d = rsquare(i) AND d > 999 THEN hs(hadsq) = 4
END IF
NEXT
IF hadprime = 2 AND hadsq > 0 THEN
FOR whsq = 1 TO hadsq
whchk = 10 - hp(1) - hp(2) - hs(whsq)
good = 1
SELECT CASE whchk
CASE 1
good = 0
CASE 2
IF VAL(MID$(digs$, 3, 1)) <> 2 * VAL(MID$(digs$, 2, 1)) THEN good = 0
CASE 3
IF VAL(MID$(digs$, 5, 1)) <> 2 * VAL(MID$(digs$, 4, 1)) AND VAL(MID$(digs$, 6, 1)) <> 2 * VAL(MID$(digs$, 4, 1)) AND VAL(MID$(digs$, 6, 1)) <> 2 * VAL(MID$(digs$, 5, 1)) THEN good = 0
IF VAL(MID$(digs$, 5, 1)) < VAL(MID$(digs$, 4, 1)) OR VAL(MID$(digs$, 6, 1)) < VAL(MID$(digs$, 5, 1)) THEN good = 0
CASE 4
good = 0
IF VAL(MID$(digs$, 8, 1)) = 2 * VAL(MID$(digs$, 7, 1)) THEN good = 1
IF VAL(MID$(digs$, 9, 1)) = 2 * VAL(MID$(digs$, 7, 1)) THEN good = 1
IF VAL(MID$(digs$, 9, 1)) = 2 * VAL(MID$(digs$, 8, 1)) THEN good = 1
IF VAL(MID$(digs$, 10, 1)) = 2 * VAL(MID$(digs$, 7, 1)) THEN good = 1
IF VAL(MID$(digs$, 10, 1)) = 2 * VAL(MID$(digs$, 8, 1)) THEN good = 1
IF VAL(MID$(digs$, 10, 1)) = 2 * VAL(MID$(digs$, 9, 1)) THEN good = 1
IF VAL(MID$(digs$, 10, 1)) < VAL(MID$(digs$, 9, 1)) OR VAL(MID$(digs$, 9, 1)) < VAL(MID$(digs$, 8, 1)) OR VAL(MID$(digs$, 8, 1)) < VAL(MID$(digs$, 7, 1)) THEN good = 0
CASE ELSE
good = 0
END SELECT
IF hp(1) = hp(2) THEN good = 0
IF good THEN
ast$ = MID$(digs$, 1, 1)
bst$ = MID$(digs$, 2, 2)
cst$ = MID$(digs$, 4, 3)
dst$ = MID$(digs$, 7, 4)
PRINT ast$; " "; bst$; " "; cst$; " "; dst$, hp(1); hp(2), hs(whsq), whchk
PRINT #2, ast$; " "; bst$; " "; cst$; " "; dst$, hp(1); hp(2), hs(whsq), whchk
END IF
NEXT whsq
END IF
END IF
permute digs$
LOOP UNTIL digs$ = h$
CLOSE 2
SUB permute (a$)
DEFINT A-Z
x$ = ""
FOR i = LEN(a$) TO 1 STEP -1
l$ = x$
x$ = MID$(a$, i, 1)
IF x$ < l$ THEN EXIT FOR
NEXT
IF i = 0 THEN
FOR j = 1 TO LEN(a$) \ 2
x$ = MID$(a$, j, 1)
MID$(a$, j, 1) = MID$(a$, LEN(a$) - j + 1, 1)
MID$(a$, LEN(a$) - j + 1, 1) = x$
NEXT
ELSE
FOR j = LEN(a$) TO i + 1 STEP -1
IF MID$(a$, j, 1) > x$ THEN EXIT FOR
NEXT
MID$(a$, i, 1) = MID$(a$, j, 1)
MID$(a$, j, 1) = x$
FOR j = 1 TO (LEN(a$) - i) \ 2
x$ = MID$(a$, i + j, 1)
MID$(a$, i + j, 1) = MID$(a$, LEN(a$) - j + 1, 1)
MID$(a$, LEN(a$) - j + 1, 1) = x$
NEXT
END IF
END SUB
The new results:
Sets sizes of size of size of
arranged as numbers primes square remainder
0 13 246 7589 2 4 1 3
0 13 468 7529 2 4 1 3
0 13 769 2458 2 3 1 4 *
0 17 359 2468 2 3 1 4 *
0 17 389 2456 2 3 1 4
0 24 359 1867 3 4 1 2
0 24 389 1657 3 4 1 2
0 24 769 1583 3 4 1 2
0 37 468 1259 2 4 1 3
0 48 769 1523 3 4 1 2
0 79 246 1583 2 4 1 3
0 79 468 1523 2 4 1 3
2 37 169 0458 1 2 3 4
5 37 169 0248 1 2 3 4 *
5 37 246 1089 1 2 4 3
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Posted by Charlie
on 2012-05-18 18:09:20 |
re(2): computer result: 11 solutions and two almost-solutions
