# Matchstick rearrangement: Zero to Hero

Below is an expression that has a value of 0.

How can you move only three matchsticks for the resulting value to be 49? Moving the left, middle and right matchstick you can make $$49$$... ... as XLIX is $$49$$ in Roman numerals!

How about LI - I - I, moving only two matchsticks? LI - I - I is $$51 - 1 - 1$$ which is $$49$$ in roman numerals.

• If you would like I could add an image? – Beastly Gerbil Aug 20 '20 at 18:46
• You may. Thank you. – Mark Tilford Aug 20 '20 at 18:50
• Added, no problem! :) Very clever answer to find it in just two matches – Beastly Gerbil Aug 20 '20 at 18:54

My solution is rather strightforward:

• Simple but effective! – Beastly Gerbil Aug 21 '20 at 15:27

Firstly orient your perspective by rotating the image a quarter turn clockwise (or equivalently, your vision a quarter turn anti-clockwise). Stand one of the lower four matches up to the right of the top 3 matches such that it represents a "0" shape, as viewed head-on. The move two of the lower three matches into a "- 1" configuration. Your movements should yield "50 - 1" which is indeed 49. The remaining match below the expression is just for emphasis or whatever. • It's a bit of a stretch to use the top of a matchstick as a zero, but good lateral thinking anyway. Gave you a +1 – Glen O Aug 21 '20 at 4:32
• How is the left bit supposed to be 50? – Harfatum Aug 23 '20 at 5:51
• The first 3 matches are a "5" and the next matchstick head represents a "0" – Dapianoman Aug 23 '20 at 7:29

It's definitely not the intended solution, but you could move it like this... Simply put, this is using the fact that H in ASCII has the hex value of 48. Therefore, H+1 would be 49 in hex. Note that the faded matchstick is "moved" off the field entirely.

Note that other such solutions can be achieved - for example, "1" has the ASCII value of 49 (in decimal), and therefore simply tilting the middle matchstick so it becomes 1/1/1/1 makes it equal to 1, which is 49 in ASCII.

Another approach bends the rules a bit, but it's fun... This is 7^2 = 49 in roman numerals. Here, I've broken one of the matchsticks while moving it. Like I said, it's bending the rules (and a matchstick)...

• Glen you definitely "Bended" the rules (see what i did there?) – Dcybroz Aug 21 '20 at 5:05
• @Dcybroz - hate to "break" it to you, but I already made that joke in the answer itself. :P – Glen O Aug 21 '20 at 5:32
• oh "snap!" i saw that. (: – Dcybroz Aug 21 '20 at 7:43

- Each vertical matchstick equals -24.5
- Each tilted matchstick is a multiplication
- Each horizontal matchstick is a subtraction

|/|—|/|

resolves to :

-24.5 × -24.5 - -24.5 × -24.5 = 0

Moving 2 matchsticks like so :

|—|—|—|

resolves to :

-24.5 - -24.5 - -24.5 - -24.5 = 49

Had to disappear a matchstick to make it work, but... (dodgy times symbol too) • Thanks for the fancy-clean edit :) – Guy S Sep 5 '20 at 9:55