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The respective sets of numbers that meet the criteria, their names and the prime factors for such numbers under 10,000 are (the first prime factor shown is the number of letters in the name):
6 SIX 3 2
33 THIRTY-THREE 11 3
253 TWO HUNDRED AND FIFTY-THREE 23 11
299 TWO HUNDRED AND NINETY-NINE 23 13
667 SIX HUNDRED AND SIXTY-SEVEN 23 29
713 SEVEN HUNDRED AND THIRTEEN 23 31
851 EIGHT HUNDRED AND FIFTY-ONE 23 37
901 NINE HUNDRED AND ONE 17 53
1007 ONE THOUSAND AND SEVEN 19 53
1081 ONE THOUSAND AND EIGHTY-ONE 23 47
3293 THREE THOUSAND TWO HUNDRED AND NINETY-THREE 37 89
3589 THREE THOUSAND FIVE HUNDRED AND EIGHTY-NINE 37 97
4009 FOUR THOUSAND AND NINE 19 211
4309 FOUR THOUSAND THREE HUNDRED AND NINE 31 139
4847 FOUR THOUSAND EIGHT HUNDRED AND FORTY-SEVEN 37 131
5587 FIVE THOUSAND FIVE HUNDRED AND EIGHTY-SEVEN 37 151
5611 FIVE THOUSAND SIX HUNDRED AND ELEVEN 31 181
6001 SIX THOUSAND AND ONE 17 353
6049 SIX THOUSAND AND FORTY-NINE 23 263
7409 SEVEN THOUSAND FOUR HUNDRED AND NINE 31 239
6 SIX 3 2
33 THIRTY-THREE 11 3
551 FIVE HUNDRED FIFTY-ONE 19 29
1147 ONE THOUSAND ONE HUNDRED FORTY-SEVEN 31 37
1271 ONE THOUSAND TWO HUNDRED SEVENTY-ONE 31 41
1643 ONE THOUSAND SIX HUNDRED FORTY-THREE 31 53
1711 ONE THOUSAND SEVEN HUNDRED ELEVEN 29 59
2263 TWO THOUSAND TWO HUNDRED SIXTY-THREE 31 73
2449 TWO THOUSAND FOUR HUNDRED FORTY-NINE 31 79
4681 FOUR THOUSAND SIX HUNDRED EIGHTY-ONE 31 151
6119 SIX THOUSAND ONE HUNDRED NINETEEN 29 211
6641 SIX THOUSAND SIX HUNDRED FORTY-ONE 29 229
8711 EIGHT THOUSAND SEVEN HUNDRED ELEVEN 31 281
8903 EIGHT THOUSAND NINE HUNDRED THREE 29 307
So the answer sets are:
33, 253, 1007
and
33, 551, 1147
DECLARE FUNCTION verify! (s1$, s2$)
DECLARE SUB ProcPiece (piece$, MajorPower!)
DATA one,two,three,four,five,six,seven,eight,nine
DATA ten,eleven,twelve,thirteen,fourteen,fifteen,sixteen,seventeen
DATA eighteen,nineteen
DATA twenty,thirty,forty,fifty,sixty,seventy,eighty,ninety
DATA thousand,million,billion,trillion,quadrillion,quintillion,sextillion
DIM SHARED unit$(19), ten$(10), major$(7)
FOR i = 1 TO 19
READ unit$(i)
NEXT
FOR i = 2 TO 9
READ ten$(i)
NEXT
FOR i = 1 TO 7
READ major$(i)
NEXT
DIM SHARED name$, num$, n
CLS
FOR n = 2 TO 9999
num$ = LTRIM$(RTRIM$(STR$(n)))
IF num$ = "0" THEN
name$ = "zero"
ELSE
name$ = ""
MajorPower = 0
DO
l = LEN(num$): IF l > 3 THEN l = 3
piece$ = RIGHT$(num$, l)
num$ = LEFT$(num$, LEN(num$) - l)
CALL ProcPiece(piece$, MajorPower)
MajorPower = MajorPower + 1
LOOP WHILE LEN(num$) > 0
END IF
name1$ = UCASE$(name$)
name$ = name1$
DO
i = verify(name$, "ABCDEFGHIJKLMNOPQRSTUVWXYZ")
IF i THEN name$ = LEFT$(name$, i - 1) + MID$(name$, i + 1)
LOOP UNTIL i = 0
l = LEN(name$)
IF n MOD l = 0 THEN
pr = 1
FOR i = 2 TO SQR(l)
IF l MOD i = 0 THEN pr = 0: EXIT FOR
NEXT i
IF pr THEN
n2 = n \ l
FOR i = 2 TO SQR(n2)
IF n2 MOD i = 0 THEN pr = 0: EXIT FOR
NEXT i
IF pr THEN
PRINT n; name1$; l; n2
END IF
END IF
END IF
NEXT
SUB ProcPiece (piece$, MajorPower)
piece = VAL(piece$)
n$ = ""
IF piece > 99 THEN
n$ = unit$(piece \ 100) + " hundred "
piece = piece MOD 100
IF piece > 0 THEN n$ = n$ + "and "
' this to be commented out for part 2
ELSE
IF MajorPower = 0 AND n > 999 THEN n$ = n$ + "and "
' likewise this
END IF
IF piece > 19 THEN
n$ = n$ + ten$(piece \ 10)
piece = piece MOD 10
IF piece > 0 THEN n$ = n$ + "-": ELSE n$ = n$ + " "
END IF
IF piece > 0 THEN n$ = n$ + unit$(piece) + " "
IF n$ > "" THEN name$ = n$ + major$(MajorPower) + " " + name$
END SUB
FUNCTION verify (s1$, s2$)
FOR i = 1 TO LEN(s1$)
IF INSTR(s2$, MID$(s1$, i, 1)) = 0 THEN verify = i: EXIT FUNCTION
NEXT
verify = 0
END FUNCTION
Based upon Enigma No. 1614, "Letters & products", by Richard England, New Scientist, 25 September 2010. |
