# Back to Matchsticks (cotton swabs)

A Matchstick puzzle with a twist.

Make the following equation right by moving 3 or less cotton swabs. ## CX = LIII + V

It is in Roman Numerals.

• Final equation must be in Roman Numerals.
• Standard Roman Numerals only please.
• No Zero.
• Re-orientation is a move.
• All modern Math signs are OK.

I uses 1 swab V, L and X use 2 swabs each C uses 3 swabs D and M use 4 swabs divide (/) and minus (-) 1 swab, multiply (x) and plus (+) use 2 swabs.
You may use multiply (X) as numeral X also.

Note : Please try not to create extra spaces to fit the swabs. Spaces require moving swabs.

• Have you decided which answer was the best one? If so, please don't forget to $\color{green}{\checkmark \small\text{Accept}}$ it :)
– Rubio
Apr 10 '17 at 16:40

I did not see this answer:

3 swabs moved:

LX - LIII = VII (60 - 53 = 7)

Explanation:

Move the top swab from C after the V. Move one of the swabs from the equal sign after the first moved swab - i.e. now we have VII. Move the vertical swab of the plus sign to make an equal sign in its place.

• Wow. That works. I didnt realize there would me more than 2 answers. I have another answer though.
– DrD
Mar 16 '17 at 13:10

Solution 1.
Moving 1 and slightly skewing 2.

CX = CV + V. Equivalent to 110 = 105 + 5.

Explanation.

Leave the part before the equal sign as it it.
From LIII take the 3 swabs/matches/toothpicks after the L (the 3 I's).
Put one above L to make it a C.
Make a V from the other 2.

Solution 2
Moving 3 swabs.

LXI = LII+IX. So: 61 = 52 + 9

Explanation

in front of the = sign, take the top swab from C and move it after X to transform CX into LXI.
after the = sign, Make V into an X by moving the first swab of the V a bit to the right.
And take one of the vertical swabs after the L (the last one) and put in in front of the X you just made, because you just freed some space in the step above.

Solution 3
Moving 3 swabs

LX = L + V + V. So: 60 = 50+5+5

Explanation:

Take the top swab from C and put it perpendicular to the first I on the right sight of the equal sign to make a +.
Now You have LX = L+II+V.
From the 2 verical swabs that make a 2 on the right side of the equal sign make a V.
Feel ecstatic.

• WOW didnt realize there could be so many. Solutions 2 and 3 do require creating spaces though. In order to create spaces you have to move the swabs. There is still one more solution there.
– DrD
Mar 14 '17 at 17:34
• Yes it requires some space but you can gain the space from other swabs you move. Mar 14 '17 at 17:49
• your first solution works for me. There is another.
– DrD
Mar 14 '17 at 21:24
• I think the first solution only requires moving one and skewing one. See the image in my answer, where I used those two the same way as you did: it's easily readable even when one of the two remains in its original position.
– hvd
Mar 14 '17 at 22:06

Moving two swabs:

• you still have to move 3, because that v is not exactly a v. Mar 15 '17 at 7:11
• @Marius The swabs in the challenge itself are off a bit as well, which tells me that's okay. The bottom swab making the L is not horizontal, for instance.
– hvd
Mar 15 '17 at 7:17
• Agree with Marius. But 3 swabs is OK
– DrD
Mar 15 '17 at 14:58

With 3 swabs

$CX/II = L + V (110/2=50+5)$

Swabs moved

III after the L in the RHS. • Well. You are creating a lot of space between X and =
– DrD
Mar 14 '17 at 16:11
• There is another way.
– DrD
Mar 14 '17 at 16:11

Boring answer. Moving and rotating one swab:

CX ≠ LII + V

• Sorry. Inequality not an answer.
– DrD
Mar 14 '17 at 21:22
• @DeepakMahulikar I suspected as much, but could you edit your question regarding "All Modern Math signs OK" to explain why not all modern maths signs are ok? Mar 14 '17 at 21:30
• @DeepakMahulikar I suggest changing "Make the following equation right..." to "Make the following equality correct...", if you agree that better presents the question. Mar 14 '17 at 21:33

Bit of a stretch, but

you stated that D requires 4 swabs. In my opinion, here are many plausible ways to make an acceptable D with 4 swabs.

So here goes...

CX = DL / V (110 = 550 / 5)

Explanation:

First move, move the rightmost I from LII to form DI. Second move, move one of the swab from the plus sign to make DL from DI (the space is available from removing one I). Final move, rotate the remaining swab of the plus sign to form a division sign.

I have a new one:

LIX - LIII = VI
or
59 - 53 = 6

Method:

1) Take the top swab of the C and place it vertically before the subsequent X, turning the number into LIX.
2) Take the top swab from the equals sign and place it vertically after the V, turning the equals into a minus, and the V into VI
3) Take the vertical swab of the plus sign and rotate it, making it into an equals sign.

• I think making + sign into = is a neat idea. But putting I before X is kind of creating new space, just my 2 cents
– DrD
Mar 16 '17 at 22:51

Two swabs moved

CX > LIII + V

Swabs moved

The two swabs in the equal are angled to form a greater than sign.

• The problem statement said 'Final equation'. An inequality is not an equation. Mar 14 '17 at 20:39
• Correct. Inequality can take only one move
– DrD
Mar 14 '17 at 21:21

If moving includes REmoving...

IX = IIII + V ; Remove 2 swabs from the C to create I, 1 from the L to create another I.

• To the best of my knowledge, IIII is not a standard Roman numeral. Mar 15 '17 at 14:14
• @Pokemon However, IIII is used on many old clocks. +1 from me. Mar 15 '17 at 15:37

One I came up with

CX = LIII + V

LX = C/II + X ( 60 = 100/2 + 10)

Move top swab from left hand side C to the right hand side L. Left hand side C becomes L and right hand side L becomes C. Then make the first I into divided sign on the RHS. Turn V into X. Total 3 moves

• I think turning V -> X will require 2 moves. Mar 18 '17 at 13:27

1 match moved:

LX≠LIII+V

Explained:

LX=60 and LIII+V=LVIII=58.

60≠58.

Who made the challenge said all modern math signs, and inequalities work.

Or...

CX=DL/V.