Answer: 27 items were metal. There were 191 entries
Worked answer
Since I received a 1-digit number of points for each type of item, there were fewer than 40 items of each type, so that 1, 2 and 3 must be the tens digits of the 2-digit numbers; the 2-digit number that starts with 1 must earn 4 points and therefore be 16, 17, 18 or 19; the 2-digit number that starts with 2 cannot be 20, 21, 22 or 23 and therefore cannot earn 5 points; and the 2-digit number that starts with 3 cannot be 30 or 31 and therefore cannot earn 7 points.
(1) 16 items = 4 points: since 6 is already used this goes with 28 or 29 items = 7 points; so the 5 must be used in 35 items = 8 points. The only possibility is:
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16 items = 4 points; 29 items = 7 points; 35 items = 8 points (80 items in total)
(2) 17 items = 4 points: since 4 and 7 are already used this goes with 25 items = 6 points. The only possibility is:
17 items = 4 points; 25 items = 6 points; 38 items = 9 points (80 items in total)
(3) 18 items = 4 points; since 8 is already used this goes with 36 or 37 items = 9 points; so the 5 must be used in 25 items = 6 points. The only possibility is:
18 items = 4 points; 25 items = 6 points; 37 items = 9 points (80 items in total)
(4) 19 items = 4 points: since 4 and 9 are already used this goes with 35 items = 8 points. The only possibility is:
19 items = 4 points; 27 items = 6 points; 35 items = 8 points (81 items in total)
(1), (2) and (3) all involve a “feed” of 80 items; but (4) involves a “feed” of 81 items. Hence, only if told that the total number of items was 81 would anyone be able to deduce the three 2-digit numbers.
