The instructions needed to do this are: |42 IF C=0 THEN l<0 |45 LET P=P l |44 LET F(P)=C |45 LET C=INT(F(P)/10) |46 LET F(P)=F(P)-10*C |47 GOTO |42 Finally, since the product contains exactly P digits, then the print loop beginning at line 170 can be changed to read FOR I = P TO 1 STEP -1. Our multiple precision factorial program, complete with all modifications discussed, now appears as: 10 DIM F(160) 20 LET L=l60 30 INPUT N 40 FOR I=2 TO L 50 LET F(I)=0 60 NEXT I 65 LET P=1 70 LET F(l)=1 80 FOR M=1 TO N 90 LET C=0 100 FOR I=1 TO P 110 LET F(I)=F(I)*M C 120 LET C:INT(F(I)/l0) l30 LET F(I)=F(I)-10*C l40 NEXT I 142 IE C=0 THEN 150 143 LET P=P 1 144 LET F(P)=C 145 LET C:lNT(F(P)/l0) 146 LET F(P)=F(P)-10*C 147 GOTO 142 150 NEXT M 160 LET S=0 170 FOR I=P T0 1 STEP -1 180 IF F(I)>0 THEN 200 190 IF S=0 THEN 220 200 PRINT F(I): 210 LET S=1 220 NEXT I 230 END Any additional improvements are left to you. Although several are possible, more efficient use of the variables in the F array is likely to be the most dramatic. The example program uses one variable to represent one digit. By allowing each variable to represent two or three digits, program speed is essentially doubled or tripled. But then there are additional problems when the product is printed, and possibly additional problems within the computation loop. Does the example have any theoretical limit on the factorials that can be computed? Does it have any realistic limits? The topic of multiple precision arithmetic will be further explored in a subsequent column. Now that you understand multiple precision multiplication, only the operations of addition, subtraction and division separate you from successfully computing SQR(2) and (PI) to at least half million digit accuracy. (To further test your knowledge of multiple precision arithmetic, why not try Contest Problem 3. - Ed.) *** Glum Glossary Punched card: A short piece of 80-channel paper tape. Program: The footprints of hundreds of bugs. Once the bugs are eliminated, the program is all that's left. *** Puzzles and Problems for Fun Mrs. Canton wanted to buy all the grocer's apples for a church picnic. When she asked how many apples the store had, the grocer replied, ”If you added 1/4, 1/5 and 1/6 of them, that would make 37." How many apples were in the store? [image] Donna bought one pound of jellybeans and two pounds of chocolates for $2. A week later, she bought four pounds of caramels and one pound of jellybeans, paying $3. The next week, she bought three pounds of licorice, one pound of jellybeans and one pound of caramels for $1.50. How much would she have to pay on her next trip to the candy store, if she bought one pound of each of the four candies? Take a 3-digit number like 200, reverse it (002) and then multiply the two numbers. The result, 400, is a perfect square (20*20 = 400). Find all such 3-digit numbers. Bill Morrison Sudbury, Mass. Can you put nine pigs in four pens so that there are an odd number of pigs in each of the four pens? *** If you have a favorite puzzle, perhaps we can print it here. Send it along!