# How many matchsticks minimum can you move to make this true?

Ok here are some rules because it would be too easy/too hard without them

1. Round to nearest 100th
2. The first number cannot be an integer
3. Needs to be an equality
4. No mixed numbers

Hint:

The equal sigh need not be aligned.

• What matchsticks? – f'' Jul 16 '16 at 3:21
• @f'' They're figurative :P – bleh Jul 16 '16 at 3:23
• Changing the rules 3 times... – Poolsharker Jul 16 '16 at 13:56
• What are "mixed numbers"? – Jonathan Allan Jul 16 '16 at 14:30
• @Poolsharker This is a lesson for me to always think a problem through. – bleh Jul 16 '16 at 15:28

Can do it moving $2$ matches (maybe there is a way for $1$?)

Take $2$ from the top of the right hand side's numerator and move them to its denominator:
Left - Roman numerals $\frac{X}{XX}=\frac{10}{20}=0.5$
Right - Tally marks $\frac{||}{||||}=\frac24=0.5$

Answer post puzzle change (without fourth rule)

Easily done for equality, moving only $1$ match

Left - Roman Numerals $I\frac{X}{XX}=1\frac{10}{20}=1.5$
Right - Roman Numerals $\frac{III}{II}=\frac32=1.5$

Easily done for equality with $2$ more matches

Left - Roman Numerals $\frac{X}{XX}=\frac{10}{20}=0.5$
Right - Tally marks $\frac{|}{\frac{||||}{||}}=\frac1{\frac42}=\frac24=0.5$

...or for a true statement, we can do it with just $1$ match

strike the equals to a not equals $\frac{X}{XX}\neq\frac{||||}{||}\rightarrow 0.5\neq2$

• Sorry, changed it. Look at it – bleh Jul 16 '16 at 3:01
• Updated to fit the changed puzzle. – Jonathan Allan Jul 16 '16 at 6:18
• Agh, your answer is better than my intended answer. I'll accept it, but find the cleverest answer if you can. – bleh Jul 16 '16 at 12:45
• I'll keep it at accepted, but I need to change the rules 1 more time :( – bleh Jul 16 '16 at 13:10

Move

0

matchsticks to make the equation true:

The left side is in Suzhou numerals, reading 4/44. The right side is $\frac{1\left|1\right|}{11}$: 1 times the absolute value of 1, divided by 11. Both sides equal 1/11.

This seems a little too simple to be correct, but..

My guess is 2.

Method:

Move 2 matchsticks from IIII to the denominator, so it becomes 10/20 = 2/4.

I'll take a stab, not sure if this is what is being asked...

1

Reason:

Move one match stick from the top of the second number to the bottom of the second number, changing the first vertical line into a V, 10/20 = 3/6

• Sorry changed it. Sorry for misconception – bleh Jul 16 '16 at 3:24
• @Bleh No problem, updated my answer. Take a look and let me know if there is something missing. – Poolsharker Jul 16 '16 at 5:09
• |/ Is not a v. Sorry – bleh Jul 16 '16 at 13:13

2

How?

X IIII
---=-----
XX I I

becomes

XI III
---=-----
XI III

by way of:

Moving one of the cross matches on the second X to the top (and straightening them out), and moving one of the 4 matches to the bottom.

Or, simply put...

11/11 = 3/3, or 1=1.

• Did you read the rules? – bleh Jul 16 '16 at 3:18
• Which rule am I breaking? – Josh Jul 16 '16 at 3:20
• Rule 2. 11/11 == integer – bleh Jul 16 '16 at 3:20
• No, 11/11 is a fraction. An integer is a whole number that is not a fraction. Just because 11/11 becomes a whole number does not mean it is an integer. – Josh Jul 16 '16 at 3:21
• No, 11/11 is an integer. What I mean, is that the 1st number not set of numerals, is not an onteger – bleh Jul 16 '16 at 3:22