Prime * Prime (Posted on 2009-08-15)

	Submitted by Charlie
Rating: 5.0000 (1 votes)
Solution:	(Hide)
The six 3-digit numbers, and their prime factorizations are: 178 2 * 89 187 11 * 17 718 2 * 359 781 11 * 71 817 19 * 43 871 13 * 67 list 5 dim Used(9) 10 for D1=1 to 9 20 Used(D1)=1 30 for D2=1 to 9 40 if Used(D2)=0 then 50 :Used(D2)=1 60 :for D3=1 to 9 70 :if Used(D3)=0 then 80 :Used(D3)=1 90 :if fnOk(100*D1+10*D2+D3) then 100 :if fnOk(100*D1+10*D3+D2) then 110 :if fnOk(100*D2+10*D1+D3) then 120 :if fnOk(100*D2+10*D3+D1) then 130 :if fnOk(100*D3+10*D1+D2) then 140 :if fnOk(100*D3+10*D2+D1) then 150 :print D1;D2;D3, 151 :Q=100*D1+10*D2+D3 152 :print prmdiv(Q);prmdiv(Q//prmdiv(Q)) 160 :endif 170 :endif 180 :endif 190 :endif 200 :endif 210 :endif 220 :Used(D3)=0 230 :endif 240 :next 250 :Used(D2)=0 260 :endif 270 next D2 280 Used(D1)=0 290 next D1 300 end 400 fnOk(X) 410 if prmdiv(X)=X then return(0) 420 N=X//prmdiv(X) 430 if prmdiv(N)=N then return(-1) 440 return(0) OK run 1 7 8 2 89 1 8 7 11 17 7 1 8 2 359 7 8 1 11 71 8 1 7 19 43 8 7 1 13 67 OK Based on Enigma No. 1552, "Prime products", by Richard England, New Scientist, 4 July 2009, page 24.

	Subject	Author	Date
	pencil and paper solution	Daniel	2009-08-15 23:10:39
	Solution	Dej Mar	2009-08-15 16:40:41