# Another Matchstick (cotton swab) puzzle

Here is another Matchstick puzzle. May be you have seen it. I have used Cotton Swabs in my picture below. I have used a digital display.

ORIGINAL: 23 x 1 = 91

By moving THREE or less swabs make the equation appear correct. You cannot completely remove swabs.

Use 2 swabs for +, one swab for -, two swabs for multiply x and one swab for divide (/).

The number Zero has 6 swabs. One has 2 swabs. Two, three, five and nine have 5 swabs each. Four has 4 swabs. Six has 6 swabs. Seven has 3 swabs. Eight has 7 swabs.

• tried to do 63/7=9, there's an extra match :\ – pie314271 Mar 7 '17 at 20:58
• $13 \times 7=91$ appears obvious, but you have to move 4 with 2 left over – nzaman Mar 8 '17 at 11:13
• $23\times 1 < 91$. – David Richerby Mar 9 '17 at 10:55

22 / 7 = PI

3 swabs moved.

• But that's not true! – Ankoganit Mar 8 '17 at 10:05
• We all know pi doesn't equal 22/7, but I'm pretty sure this is the intended answer ;) – Pokemon Mar 8 '17 at 12:04
• Ewww, I so hope this is wrong. – Gareth McCaughan Mar 8 '17 at 15:41
• @BrianJ First swab: Turn 3 into 2. Second swab: remove descending diagonal from X and turn first 1 into 7. Third swab: Turn 9 into P. – Victor Stafusa Mar 8 '17 at 15:58
• That is why I used the word "make the equation appear correct" – DEEM Mar 8 '17 at 16:55

3 moves.

2+3x1=5 Move the one over to make the plus sign and move a stick on the 9 to make it a 5.

• Well how about that – n_plum Mar 8 '17 at 2:41
• Brilliant and almost certainly the correct answer! – Xenocacia Mar 8 '17 at 2:58
• Good answer, however there is no space between 2 and 3. Doing as you describe, we need to move the entire 2 to the left, and that's moving more than 3 matches for sure. – Pokemon Mar 8 '17 at 3:19
• @pokemon: not sure about OP's intention, but for such puzzles the spaces between numbers is generally taken as irrelevant. Of course, if OP has an answer that accounts for this it only makes this puzzle that much more devious...! – Xenocacia Mar 8 '17 at 5:23
• I may be wrong, but the fact that OP explicitly provides the screenshot of the swabs makes me think that the position is relevant. – Pokemon Mar 8 '17 at 6:14

By moving only one match/swab, I can turn $23 \times 1 = 91\;$ into:

$23 \times 1 \neq 41$

Other possible solution moving only one swab:

$23\;/\;1 \neq 91$

Other possible solution moving only two swabs:

$23 \times 1 < 91$

And they are all correct. Yay!

Ok, I know that this is not an equation anymore.

• Ingenious, I will give you that. But the question says equation. Yours are in-equations. – Marius Mar 8 '17 at 10:22
• @Marius that is the reason why I added the last spoiler block. – Victor Stafusa Mar 8 '17 at 12:10
• Oh. Sorry. I missed that. I acted like any other internet user. I see something wrong, I stop reading so I can tell that person that he/she is wrong. I love jumping to conclusions. :) – Marius Mar 8 '17 at 12:11
• I joined this stack community just to upvote your answer. Genius. – Reinstate Monica Cellio Mar 9 '17 at 8:38

I am not sure how legal this is since you didn't specify much rules, but I can solve it in one move.

If you walk around/rotate 180 degrees it turns into:

16 = 1 x E2

If you take that "E"/backward 3, and move it onto the 1, you get an 8, which leaves you with a solved solution of:

16 = 8 x 2

• Using your 3 moves to move the three? I love it. It would be 5 individual moves, though, unless this is lateral thinking. – Matt Mar 7 '17 at 21:20
• That's why I'm not sure if this counts, it was specific as to whether whole movements or rotations etc counted.. Like would spinning the x to a + count as a move? – n_plum Mar 7 '17 at 21:40
• The problem with this solution is that OP specifies a "6" is made with 6 swabs while a "9" is made with 5 swabs, so an inverted "9" does not turn in to a "6". – A. I. Breveleri Mar 8 '17 at 1:54
• It still looks like a 6 though :P Creative points albeit not a right solution I guess – n_plum Mar 8 '17 at 2:23

I can do it by moving 3 single matchsticks to yield:

$09\times1=9^{1}$

In this solution I

Remove the bottom matchstick of the second '1' to make it 'to the power of one'.

While this could be considered bending the rules I personally think it is acceptable because

The smaller number 'appears correct' (more so than using two matchsticks as described).

3 x 3 x 1 = 9

To do this:

Move the bottom-left swab of the 2 across so it becomes a 3. Then move the two swabs of the 1 to form an "x" between the two 3s. Similar to @AstroMax's solution.

24+7=31

Process:

Move 1: Making 23 as 24, you need to do 3 -> 4 i.e moving one swab up and removing the top one. Move 2: Making 1 as 7, put the one removed from 3 to the top. Move 3: Making 91 -> 31 , just remove the left most swab of 9 to the bottom. Making the multiplication sign as plus is just orientation.

Another one:

13 x 7 = 91

Process

Move top of 2 over 1 (to make it 7). Move left of 2 side and remove others.

• I think, orientation is considered as a move here. Isn't it? – Techidiot Mar 8 '17 at 10:37
• Orientation is a move – DEEM Mar 8 '17 at 16:57

92-1=91

Alterations:

1) Taking a stick from 'x' making it '-' and placing it in 2.
2) Making one more adjustment will make the 1st digit appear as 9.
3) Adjust bottom right stick to the left making it a 2.

• To make a "-" from "x" requires a 2 moves. – Techidiot Mar 8 '17 at 10:32

There is one easy answer guys :

27 / 3 = 9

all what you have to do is :

23 X 1 = 9 becomes 27 / 3 = 9

remove 2 swabs from the '3' to make it 7, and remove 1 swab from the 'X' to make it '/', then add the 3 swabs to '1' to make it a '3'.

;-)

• It looks to me like you have two swabs left over. – Gareth McCaughan Mar 8 '17 at 15:43
• I don't think so Gareth, I added an explanation on my answer to make it clearer ;) – imAProgrammer Mar 8 '17 at 15:49
• So then what happens to the "1" at the end? (The equation starts off saying 23x1=91, not 23x1=9.) – Gareth McCaughan Mar 8 '17 at 16:02
• 27/3 = 91 is a != @GarethMcCaughan Is right that you're missing swabs. – n_plum Mar 8 '17 at 16:06
• Ah sorry I didn't see the last '1'.. I will think of another solution. thank you guys ^^" – imAProgrammer Mar 8 '17 at 16:09

16=1×E2,

which is either

16=1×E×2 (solved for E=8),

or

16=1×E2 (solved for E=4).

• I don't think you can just change a number to a variable and solve for it. – Herb Wolfe Aug 23 '17 at 15:34