Here is a matchstick puzzle with TWO (possibly more) solutions.

Matchstick Puzzle

There are two types of matchsticks.

1 Short (eight and = sign) Total 9

2 Long ( All ones) Total 4

Please move 3 matchsticks and make the equation right.

Rules

  • Must move 3 matchsticks, one or two moves not allowed.

  • Cannot remove matchsticks

  • Must move at least one of each type ( either 2 long ones and 1 short or 1 long one and 2 short)

  • No < or > or "not equal to" allowed

  • No looking from the top or mirror image

  • Except for 1, other digits (2,3,4,5,6,7,8 and 9) use short match sticks only.

I have 2 solutions: One kind of obvious but another requires lateral thinking which is what I am looking for. Please give both the answers together

While I appreciate the obvious solution/s there is still a Lateral Thinking solution there

HINT

Think letters

  • 1
    Is it allowed to write '1' with two short matchsticks ? – Evargalo Oct 18 at 15:14
  • I am sorry but no. Like I said 1 is 1 long matchstick – DEEM Oct 18 at 15:37
  • 2
    What about other symbols? Does = have to be small matchsticks? What about + and -? – Golden Dragon Oct 18 at 15:41
  • 1
    Don't be sorry ! The rules are yours to choose, I just wanted to make sure. – Evargalo Oct 18 at 15:41

13 Answers 13

up vote 7 down vote accepted

Solution 1:

    _   | | | = | | - | | |_| | | |    

The minus sign is formed from:

the short match removed from the $8$ to make it into a $0$.

Solution 2 - Lateral thinking:

    ____ _  | | _| = |   | | |_| |_      
The vertical legs of the $\pi$ and the left side of the $C$ are formed by long matchsticks that have not been moved. The third long matchstick from the left has been moved to form the top of the $\pi$ and the two short matchsticks from the $8$ form the top and bottom of the $C$.

Note: It's not easy to make monospaced text inside a spoiler tag!

  • Number 1 is shown as 2 matches. The rule says 1 only. Is that a typo? – DEEM Oct 18 at 18:20
  • Unfortunately you've moved 4 matches – Ben J Oct 18 at 18:21
  • Oops, you're right, I did move 4 matches for this one! – Dan Henderson Oct 18 at 18:51
  • 1
    I think I may have beat you to that answer but nice try – gabbo1092 Oct 18 at 18:55
  • 3
    Your second solution is what I was looking for @Dan Henderson – DEEM Oct 19 at 18:13

The mathematical (a.k.a. obvious) solution:

Move the first two 1 down so as to get $1^{1^{18}}$
Then take the middle segment of the eight and make it a minus sign so as to get $1^{1^{-10}}$
Now your equation is correct.

(this is only one among many other solutions based on the same idea)

The lateral-thinking solution:

  • The second one is brilliant! great OOBox thinking. Wish I had thought of that – DEEM Oct 19 at 14:57
  • Thank you @DEEM, but unfortunately that means this is not the expected answer... I look forward to seeing it, then. – xhienne Oct 19 at 19:57

Possible solution:

Move a long stick from the left next to the 1 on the right making 118=11. Then move the small stick from the middle of the 8 turning it to a 0 and move it next to the 11 making 110=11- . Then move another long one after the minus making 10 = 11 - 1

Possible Lateral Thinking answer:

move a small stick from the 8 making a minus sign leaving 111-6=1. Then move a large stick on the right to be at an angle turning it leaving 111-6 = \ . Then move one of the large sticks fro the left over at an angle creating a V, leaving 11-6 =V which is the roman numeral for 5.

I'll take the mathematical solution from https://puzzling.stackexchange.com/a/74090/33433.

Lateral solution:

Move the two rightmost short sticks from the 8 to between the first two long sticks on the left, sideways, at the top and bottom, forming the letter O. Move (slant) the 3rd long stick from the left with the top resting against the 2nd long stick from the left and the bottom resting against the bottom short stick of the former 8 Results in the figure: ONE = 1, though the N shares lines w/the O and E.

I may have a solution

If you make the 8 a two, move one of the 1s over to the right side(to make 11), subtract a 12 from a 1(on the left), and take the leftover stick from the two to be -11.

To look like

1-12=-11

  • 1
    Looks nice to me. – Evargalo Oct 18 at 15:42

move the middle long matchstick on the left side over the top of the two others to make ∏ (pi). remove two matchsticks from the 8 to make two, and move them over the long match stick on the other side to make tau (which looks a lot like just a T) tau is defined as exactly 2 pi. because pi is not a digit, this can use implicit multiplication

__ _ ___
|| _| = |
|| |_ |

  • On the right track @Destructible Lemon. What else can "pi" do that is simpler? – DEEM Oct 19 at 11:52

NEW Solution:
Lateral

shift the first | to the left a bit: | ||8 = |
move the right two shorts of 8 to make L and N of the left 3 | pieces.
* _ _
| | | |_ = |
|_ | | |_ |
Or: LN E = 1 (ln e = 1 property: https://en.wikipedia.org/wiki/Natural_logarithm)
Note: Don't know how to format properly, so * is to make the spaces listen.


Solution 1:

Move the first large stick over to the left to create a space: 1 118 = 1 Move second stick over to left too: 11 18 = 1 Move short stick from 8 to between new numbers: 11 - 10 = 1 I found it odd that you didn't express 0 in your list of numbers and the pieces used to construct them though.

Solution 2:

Move second large stick to left of first: 11 18 = 1 Move top left short stick from 8 to lateral position between new numbers: 11 - 1(reverse six) = 1 Move bottom right short stick from (reverse six) to lateral position on right side of equation: 11 - 12 = -1

  • Ah, looks like these are similar to others' answers. Woops. – Dorrulf Oct 18 at 16:45
  • I love the one using the math function – Swiss Frank Oct 21 at 16:29

Possible answer with some more twist:

enter image description here
Move the two leftmost long matches down and to the left, move and rotate 45 degrees the middle short match from 8 next to the third long match to form square root sign. Result reads "11 to the power of the square root of 0 equals 1".

Based on the initial rules which I have observed

Rules:

Must move 3 matchsticks, one or two moves not allowed.
Cannot remove matchsticks
Must move at least one of each type ( either 2 long ones and 1 short or 1 long one and 2 short)
No < or > or "not equal to" allowed
No looking from the top or mirror image
Except for 1, other digits (2,3,4,5,6,7,8 and 9) use short match sticks only

Lets start with some basic principles:

Assumption 1:

Since minimum 1 long stick has to be used, this implies that the following numbers are not possible >


4 - 3 short sticks need to be moved
7 - 3 short sticks need to be moved

Assumption 2:

Same matchstick cannot be moved back & forth (counts as 2 moves to reach same result), but moving a difference matchstick does (i.e. I can move 1 long matchstick from left to right, and move another long matchstick from right to left of Equal sign

Assumption 3:

Mathematical operators (eg +, - , = ) can be formed by either long or short sticks, especially + & = can be formed by a mixture of long & short sticks.

Legend: L - Long matchstick S - Short matchstick

Possible solutions:
Solution 1 (2L1S):

11 - 10 = 1
Step 1: Move 2nd L on left of Equal sign to most right
Step 2: Move Original L on right of Equal sign to left
Step 3: Move centre S of the 8 between 2nd and 3rd L on left of Equal sign (forming 11-10)

Solution 2 (1L2S):

11 - 0 = 11
Step 1: Move 3rd L from left of Equal sign to move right
Step 2: Move centre S to bottom of = sign
Step 3: Move top S of Equal sign to left of 0 (making it 11 - 0 = 11)

Pretty sure there are more than 2 solutions which these are possible ....

  • Guilty as charged! Amended – Kryesec Oct 19 at 0:39

Does this count?

119 != 1 (where "!=" is the inequality sign, an equal sign with a slash through it)

It's my first time responding to something like this, so I may be way off here.

  • "Rules: No < or > or "not equal to" allowed" and this is invalid. – u_ndefined Oct 20 at 14:13
  • Fair enough. Thank you. – KlaymenDK Oct 21 at 10:30

ONE = 1 is possible by tilting the second match from the left, then moving while bending the two rightmost matches of the 8, or exploiting any natural bend they have for greatest effect.

Lateral thinking solution:

Move 2nd long stick to make 'Pi' and move 2 left corner small sticks from 8 to make it 'd' and attach them to right hand side to make it 'C'. So, Pi * d = C (circumference = Pi * diameter)

Image of solution:

enter image description here

got idea from @Destructible Lemon's answer so, thanks to her;)

  • i'm a "her", thank you very much – Destructible Lemon Oct 22 at 10:10
  • sorry for that, edited:) – Preet Oct 23 at 1:15
  • Please check @Dan Hendorson's answer on Oct 18. Same I think. – DEEM Oct 24 at 20:31
  • Yeah , you are right exact same, wondering how i missed that – Preet Oct 25 at 1:45

118 ≥ 11 doesn't include the three specifically-mentioned banned special characters.

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