0s make 120

Logic Level 2

What is the fewest number of 0s that are needed to make the number 120, using only two of the operators from the set $\{+, -, \times, \div, !\}$ between the 0s?

Details and Assumptions :

Parentheses are allowed, but concatenating digits is not.
You may use each of the two operators selected multiple times.

The answer is 4.

6 solutions

Rohit Ashiwal
Oct 2, 2016

$\Large ((0!-(-0!)-(-0!))!-0!)! = 120$

The answer is 4.

Change ker diya mene

Rohit Ashiwal - 4 years, 8 months ago

Rishabh Sood
Jan 25, 2016

Explaining further: The two mathematical operators to be used are factorial(!) and addition/plus(+) Now, Factorial basically is as follows: For example factorial of 5 will be like 5!= 5x4x3x2x1=120 But, over here we have only zeroes, so it is necessary to know that 0!=1. Thus, we will have (0!+0!+0!+0!+0!)!=> (1+1+1+1+1)!=>(5)!=>120(as we saw above) So, N(that is the number of zeroes)=5 P.S. If u like my solution please like Ask for any further queries relating this

The fewest is "4" not 5

Here's why ((0!+0!+0!)!-0!)!=((1+1+1)!-1)!=(3!-1)!=(6-1)!=120

Caeo Tan - 5 years, 4 months ago

You can only use 2 operators, u used 3

Victoria Guo - 5 years, 4 months ago

Yeah true! See my solution is correct,#thanks victoria

Rishabh Sood - 5 years, 4 months ago

@Rishabh Sood – We can still use 2 operators and 4 zeros to make 120: ((0!-(-(0!))-(-(0!)))!-(0!))! = ((1-(-1)-(-1))!-(1))! = ((1+1+1)!-(1))! = (3!-1)! = (6-1)! = 5! = 120

Mu'amar Musa Nurwigantara - 5 years, 4 months ago

@Rishabh Sood – Hey, who downvoted your solution. It is correct

Ashish Menon - 5 years, 4 months ago

Addition and subtraction are the same, subtraction is adding a negative number.

Brian Wang - 5 years, 4 months ago

and you used a negative 0. DNE.

Joshua Coddington - 5 years, 4 months ago

Use only 2 operator but u have used 3 I.e +,-,!

Pâwâŋ Mukhi - 5 years, 4 months ago

yeah we can use 3 operations that's good..

zubair ahmad - 5 years, 4 months ago

So guys, concluding we can use 5 zeroes minimum. Thus me and those who answered 5 win!

Rishabh Sood - 5 years, 4 months ago

yeah that's right....

Anup Dhawan - 5 years, 4 months ago

Did it the same way dude

Ashish Menon - 5 years, 4 months ago

Prince Loomba
Jan 25, 2016

(0!+0!+0!+0!+0!)!=5!=120

This is 10 mathematical operators, but only 2 kinds of mathematical operators.

Brian Wang - 5 years, 4 months ago

OK I have clarified it more. Thanks.

Prince Loomba - 5 years, 4 months ago

Give me a hi5 bro!(prince)

Rishabh Sood - 5 years, 4 months ago

I am not prince, but I give a hi5 rishab lol

Ashish Menon - 5 years, 4 months ago

Keil Cerbito
Jan 30, 2016

I think it should be four.. we have the same answer by Mu'amar Musa Nurwigantara .. ((0!-(-(0!))-(-(0!)))!-(0!))!

Thanks. I've updated the answer to 4. Those who previously answered 4 has been marked correct, while those who previously answered 5 has been marked wrong.

In future, if you spot any errors with a problem, you can “report” it by selecting "report problem" in the menu. This will notify the problem creator (and eventually staff) who can fix the issues.

Brilliant Mathematics Staff - 4 years, 8 months ago

Ashish Menon
Mar 9, 2016

$[cos (0)+ cos (0)+cos (0)+cos (0)+cos (0)]!$
= $[1+1+1+1+1]!$
= $5!$
= $120$ . $_\square$

Emil Choparinov
Jan 30, 2016

(cos(0)+cos(0)+cos(0)+cos(0)+cos(0))!=(1+1+1+1+1)!=5!=120

cos is not in the given range of operators

Prince Loomba - 5 years, 4 months ago

0s make 120

The answer is 4.

6 solutions

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