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It takes one matchstick to make the "I" symbol, two to make the "V" symbol, two to make the "X" symbol, two to make the "L" symbol, and four to make the "M" symbol (I'm excluding "C" and "D" as they are curved shapes).

I got 45 without multiplication... I - (1)

II, V, X, L - (4)

III, IV, VI, IX, XI, LI - (6)

VII, XII, XV, XX, XL, XII, LV, LX, M - (9)

VIII, XIII, XIV, XVI, XIX, XXI, XLI, LIV, LVI, LIX, LXI, MI - (12)

XVII, XXII, XXV, XXX, XLII, LVII, LXI, LXV, LXX, MII, MV, MX, ML - (13) Although the above doesn't include the fact that some Roman numerals can be multiplied by 1,000 by adding a single horizontal line over them, which gives additional symbols to work with:

Three sticks: (V), (L), (X) - (3)

Four sticks: (IV), (VI), (IX), (XI) - (4)

Five sticks: (M), (VII), (XII), (XV), (XX), (XL), (LV), (LX) - (8)

Six sticks: (VIII), (XIII), (XIV), (XVI), (XIX), (XXI), (XLI), (LIV), (LVI), (LIX), (LXI), (MI) - (12) For a total of 27 more symbols. Using the info from the first part makes this easier - anything using three sticks can be combined with anything using one, two, or three sticks, which makes for (3*11) more numbers. Anything with four sticks can be combined with anything using one or two sticks, which makes for (4*5) more choices. Anything using five sticks can be combined with anything using one stick, which makes for (8*1) more choices. So, in total: 45 + 27 + (3*11) + (4*5) + (8*1) = 133

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14y ago
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Q: How many roman numerals can be made using 6 matchsticks?
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