perplexus.info :: Logic : Pandigital Recycling Points

Pandigital Recycling Points (Posted on 2009-05-31)

Richard took glass, metal and plastic items to the recycling plant and received 1 "green point" for every 4 items in each category that he brought in. In any category, items in excess of a multiple of four were not counted, so, for example, if he brought in 21 glass items, 30 metal items and 43 plastic items, he'd earn [21/4] + [30/4] + [43/4] = 5 + 7 + 10 = 22 green points. (The [] square brackets indicate the floor function--the greatest integer not exceeding the value within.)

One week he brought in a 2-digit number of glass items, a larger 2-digit number of metal items and a still larger 2-digit number of plastic items. For each class of item he received a 1-digit number of green points.

Among the three 2-digit numbers and three 1-digit numbers involved, all the non-zero digits, 1 through 9, appeared exactly once.

If I told you the total number of items brought, you'd be able to deduce how many were glass, how many were metal and how many were plastic.

How many of each category were there?

Submitted by Charlie

Rating: 4.0000 (2 votes)

Solution: (Hide)

All the possibilities of 2-digit quantities of items with 1-digit quantities of green points each which satisfy the all-9-positive-digits criterion are listed below with the number of green points for each category and the total number of items brought:

16 29 35 4 7 8 80 17 25 38 4 6 9 80 18 25 37 4 6 9 80 19 27 35 4 6 8 81

Only 81 appears only once in the list as a total number of items. So there were 19 glass items, 27 metal items and 35 plastic items.

FOR a = 10 TO 37 FOR b = a + 1 TO 38 FOR c = b + 1 TO 39 ap = a \ 4 bp = b \ 4 cp = c \ 4 s$ = LTRIM$(STR$(a)) + LTRIM$(STR$(b)) + LTRIM$(STR$(c)) + LTRIM$(STR$(ap)) + LTRIM$(STR$(bp)) + LTRIM$(STR$(cp)) good = 1 FOR i = 1 TO 9 IF INSTR(s$, LTRIM$(STR$(i))) = 0 THEN good = 0 NEXT IF good THEN PRINT a; b; c, ap; bp; cp, a + b + c END IF NEXT NEXT NEXT

From Enigma No. 1542, "Recycling points", by Richard England, New Scientist, 25 April 2009, page 24.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Answer	K Sengupta	2023-11-17 11:13:26
re(2): analytic solution	Charlie	2009-06-03 12:33:02
re: analytic solution	varadarajan	2009-06-03 05:26:11
No Subject	Dej Mar	2009-05-31 18:44:40
analytic solution	Daniel	2009-05-31 13:30:35
computer solution	Daniel	2009-05-31 13:07:45

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