9 9 9 9 = 1 0 0
What is the fewest number of operators ( + , − , × , ÷ ) needed on the left hand side of the equation to make the statement true?
Details and Assumptions :
For example, if the equation 9 + 9 + 9 ÷ 9 = 1 0 0 is true, then you have used 3 operators: one division and two additions.
You are allowed to concatenate the digits, but it does not count as an operation. (That is, you can treat 9 9 as 99.)
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Correct.
where in the RULES OF BODMAS does this is being considered? you can not just combine two 9's as 99, 99=9(10)+9 not any 9 9 that's totally different!
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I totally agree with you. This is rather guessing than math reasoning.
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Please read details and assumptions. If you have proper vision , you can see that it is written "You are allowed to combine the digits."
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@Nihar Mahajan – concatenate* then. not concate. that's the correct term
@Nihar Mahajan – Then why not 999÷9?
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@Danny Turner – You should prob make sure you can do arithmetic before posting that
@Nihar Mahajan – You're right, but I don't change my mind. This is not real math reasoning. I'm not a member of Brilliant for this kind of problem. I won't try to answer to any similar question in the future. Of course, this is OK for people who have interest and agree to answer. Thank you for your attention. By the way, are you really 14? On your photo, you don't look as 14. I suppose that you use the photo of another and anonymous or famous person. Regards.
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@Louis-Marie Gaulin – This problem is not in the math category; it is in logic. All of these problems are about thinking outside of the box.
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@Andy Luce – Being logical isn't thinking outside the box. Thinking outside the box is saying 2+3=5, but if the 2 ='d 3 then 2+3=6. Logically speaking is saying, 2+3=5. It's black and white.
@Louis-Marie Gaulin – If you have any problem with the combining of digit , you are free to express your thought to the person who "posted" this problem rather than telling it to me. I am really 14 and I am a fan of Robert Downey Jr. I have intentionally kept him as my profile pic.
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@Nihar Mahajan – My intention wasn't to express my thought "against" you as one of the guys who found the answer. I simply commented on a post by Caeo Tan, not "against you". Please don't take it personal. I now identify Robert Downey jr. on your photo. Thanks.
@Louis-Marie Gaulin – I don't know what your perception of "Math reasoning" is, but i suggest you improve your logical reasoning first, you don't really make any sense. Concatenate the digits, Whassa pwablem?
Please read details and assumptions. If you have proper vision , you can see that it is written "You are allowed to combine the digits."
the question said that you could concatenate the digits if you want. So it's perfectly correct.
The question description says you can. But yes, it is weird that you have to do that in this case, as you're NEVER allowed to do that in real life.
9x9=81+9=90+9=99x9=891+9=900/9=100
The answer is really close :P
Should be 9 ÷ 9 + 99 or 99 + (9 ÷ 9). Otherwise this could be considered (99 + 9) ÷ 9...
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The statement is correct, because we follow the Order of Operations .
No...Order of operation mult/div first then addition/subtraction... 99+9/9 is the same as 99+ (9/9 )
I tried to input the answer but it wouldnt let me, it kept saying I had to have an integer, I had 9÷9+99=100
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The answer is how many operators are at least needed.
I do exactly the same as you do.
can't I do 999 : 9?
its true because the rule allow as to concatenate the numbers.. haleer!
There's no plus 1
the solution might be right if you can insert brackets- (9/9). i like the thinking
you cannot combine two nines like this
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Please read details and assumptions. If you have proper vision , you can see that it is written "You are allowed to combine the digits."
99- (9/9) = 100 is an answer, but following PEMDAS, the parenthesis is not needed, so we can rewrite the problem as 99- 9/9 = 100. Thus, the least amount of operators needed would be two ( the subtraction and division ).
Good job. To ensure that you have indeed found the minimum (and not just a possible bound), you should explain why the answer is not 1.
It must be addition, not subtraction. It's like you're saying: 99- 9/9 = 98
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For me it must like this 99-(9/-9) or 99+(9/9) your right.. !!!
it is in bracket so subtraction will change to addition ! 99-(9/9) = 100
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that makes no sense whatsoever. even with the brackets, the answer is going to be 98
it will not change the equation even it has bracket!!!!!!! it will fall like this 99-1 =98
+, not -. With -, it seems like you're saying 99 minus 1 is 100.
The above replies are right, you probably don't realize you are subtracting instead of adding. Your answer would turn out at 98 instead of 100 :O
I assumed adding a decimal was allowed and submitted 1 as an answer: (99/.99=100). Disappointed I am.
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It is not allowed. You cannot randomly add decimals to your calculations.
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If this problem allows you to combine two numbers, you can add decimals.
I have submitted the solution as 99 + 9/9 = 100. it is refusing to accept telling that the answer must be an integer. But answer is given as 100 and i have use minimum operator, right!
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The answer is 2
You actually gotta answer whats the fewest number of operations necessary, not which operations. Thus, the answer is 2.
it should be 99+(9/9)
I'm sorry, I don't actually get it... Wouldn't 99-9/9 be 98? So, Why would that be the answer?
the above answer is 98, not 100
Why is 2 the minimum? Why not 1 (or Zoidberg)?
This is because 9/9 also contains one operation which is 9÷9
Sravanth, please be responsible when setting the level of a problem. This problem is clearly not a level 5. If you think that this is at the difficulty of a level 5 problem, that will make me question if you do deserve to be at level 5.
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I'm sorry for that sir. In future I'll set the level carefully. I just wanted to see how good the people will be at solving it. I am sorry for inconvenience caused by me
This is an improper way to write a fraction. You should only write the proper fraction a c b when 0 < b < c .
It would be right if you write 9 9 + ( 9 ÷ 9 ) .
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Thanks! So is it correct to write the solution as @Nihar Mahajan had written?
Actually @Mehul Arora posted a report saying, 9 9 + 9 9 will become, 9 9 ( 9 9 )
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Yes, Nihar's one is correct. It's only true if the fraction is a proper fraction, that is the numerator is less than the denominator.
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@Pi Han Goh – Thanks! I had written the correct solution earlier, but due to Mehul's report, I got confused and . . . ;P
I know I'm going to get yelled at for this, but I think it's funny I got the correct answer incorrectly.
I understand you are able to CONCATENATE, but I didn't realize you are not able to UNCONCATENATE (i.e. Split the 100 into 1 00.
My solution was:
99 - 99 = 10 * 0
I know it's incorrect. I just think it's interesting.
It's not incorrect. That truly is thinking outside of the box. I don't see why one would say that's incorrect. 👏👏👏
It's incorrect as operations can only be used on the left-hand side.
99+(9-9)! =100 ergo god
99+9/9=99+1=100
[99 is combined as written that you can combine]
9/9+99=100. 9/9=1,1+99=100. Easy Peeasy Lemon Squezy. im 11 years old by the way...
(999 - 99 ) : 9 = 100
99+9/9=100 (2 operations)
It cannot be one as none of the possible solutions are 100;
999+9=1008
999-9=990
999/9=111
999x9=8991
99+99=198
99-99=0
99/99=1
99x99=9801
9-999=-990
9/999=1/111
9 9 - 9 9 = 1 x 0 0? That'd be two then? :)
The answer is 2. => 99+9/9
99+(9/9) - 2 operators
99+1=100
an easier solution is 999 ÷9= 100 so it would be 1
999 ÷ 9 = 111.
99 + 9/9 = 99 +1 = 100 using 2 signs.
((9/9) +9)*((9/9) +9)= 10 *10 =100
9 divided by 9 = 1 + 99 = 100
9/9+9 9=1+99=100 by PEMDAS
99+9/9 =100 that is two operations.
9/9=1+99=100 so the operator is 2
99 + (9 / 9) = 99 +1 = 100
This would be simpler if we just address the problem as if it were code in Java. Ex: 9 9 9 9 = 100 we could solve this quite easily if we concatenate the digits into 9999 and used only one operator. 9999 != 100. Simple.
9/9 = 1
1+99 = 100
2 operations.
First, we could do 9/9 on the two left-most nines to get 1. Then we add with the remaining concatenated two nines (99). 1 + 99 = 100. In other words, 9/9 + 9 9 =100
9÷9 +99=100. Easier expression as the division is first in the equation and there was no need to change to a fraction.
9/9 + 99 = 100
two operators used
this solution makes sense.
Written in the question: With your answer, define N as the least amount of mathematical operators used. Find N.
I think, the value of N is not 'least', it is 'only'.
PEMDAS = Please excuse my dear aunt Sally. BODMAS = Billy only does math after supper ??? Or is there already a better memory aid?
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9 9 + 9 ÷ 9 = 9 9 + 1 = 1 0 0