It's closer than you think
1 2 3 4 = 1 0 0 0
Without touching the right side of the equation, find a way to make the equation above true. You are only allowed to use mathematical operators like addition, subtraction, multiplication, division and parenthesis, percentage, and factorials only.
With your answer, define N as the least amount of mathematical operators used. Find N .
Details and Assumptions :
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As an explicit example, if the equation 1 ÷ ( 2 + 3 ) 4 ! = 1 0 0 0 is true, then you have used 4 operators: one division, one addition, one parenthesis, one factorial. In this case, N = 4 .
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You can combine the digits as well. i.e.: 1 2 + 3 4 .
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You must keep the digits in order (from left to right). 1 + 2 + 3 × 4 is valid while 1 + 2 − 4 ÷ 3 is not valid.
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BODMAS applied.
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You need a number before the percentage sign. For example. 1 2 3 4 + % is invalid while 1 2 3 + 4 % is valid.
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Exponentiation is allowed.
The answer is 5.
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4 solutions
Moderator note:
Nicely done. I've changed the answer from 7 to 5. Those who answered 5 will be marked correct.
@Svatejas Shivakumar , we really liked your comment, and have converted it into a solution. If you subscribe to this solution, you will receive notifications about future comments.
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Please add exponentiation to the list of operators. As I read the description it is not allowed.
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Thanks. I've updated the problem statement.
That's pretty amazing :)
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Calvin Lin That is indeed a pretty amazing solution. But don't you think the problem would be better if we assign a distinct number to each operation and ask what the smallest number can be formed by entering the number assigned to each operation in order of the solution. For example for the solution above, if addition is assigned as 1 ,subtraction as 2, multiplication as 3, division as 4, parentheses as 5, percentage as 6 and factorials as 7,the answer would be 56234.
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Of course, there are multiple ways of asking the question. We do not have full control over the answer format that someone decides to post the problem in.
Furthermore, problems like this would often allow for multiple answers, whereas we currently only accept 1 value.
Awesome! Upvoted!!
I tried 1/((2+3)%*sqrt(4)%) Yeah, it breaks some rules, and it's not the minimum, but I'm happy enough to have found something :P
I am not getting it how 100^(2/3)=1000
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Oh, that's a great observation!
Can you post a similar problem, just remove the 4?
1%=1/100. (1/100)^(-3/2)=100^(2/3)
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(1/100)^(-3/2)=(1/100)^(2/3)=100^(-2/3)=100^(3/2)=1000
My solution: 1/(((2*3+4)%)%)= 1000
It states in the directions "You need a number before the percentage sign. For example. 1234+ % is invalid while 123 +4% is valid." Your second percent doesn't have a numerical value. In this case (with the way the problem was worded of course) % is not an acceptable operation. It is used instead to turn a number into a smaller value. 10%% doesn't work.
( ( 1 + 2 ) ! ) ! ÷ ( 3 × 4 ! ) %
Moderator note:
This solution has been marked wrong.
Oh, if decimal points are allowed, and count as an operator, we can do
1 . 2 ÷ 3 % ÷ 4 %
That's 5!
How about 1 ÷ ( ( 2 × 3 + 4 ) % ) %? This results in N = 7
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Oh no!!!! I thought I ran through all possible scenarios!!
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Is 1%% allowed? IE in Dhruv's solution, can we just do
1 ÷ ( 2 × 3 + 4 ) % % ?
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@Calvin Lin – Sigh.... yes. (I'm curious why I didn't receive notification for this).
Great job!! I've updated the answer to 7.
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Thanks. But don't you guys think that we are still short of a proof?
I mean there can be values of N still less than 7 .
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@Dhruv Bhasin – Of course. The proof part is the hard part of this type of question, and I think that we would have to run through every single possibility.
I know that 10 is an incorrect answer, and so 7 is much more likely to be correct, hence I've updated the answer to 7. If someone else comes along with a possibility for 5, then I would update it too.
Not sure how this should really look, but I found 1%^-2 ÷ (3!+4) = 1,000. Still N=7 though.
What about 1 ÷ 2 % ( 3 ! − 4 ) , which looks like to me 5 operators?
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Your operation is not clear, do you mean a ÷ b c = a ÷ b ÷ c or a ÷ ( b × c ) ? Either way, I'm not getting 1000 as the answer.
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I think he means 1 ÷ 2 % × ( 3 ! − 4 ) = 1 0 0 .
I think according to BODMAS rules, first all the percentages of numbers and factorials of numbers are evaluated, so that 2% becomes 0.02 and 3! becomes 6, then what's parentheses are evaluated, so that (6-4) becomes 2, and then products and divisions are done. If this last stage is done without further parentheses, then order doesn't matter, we have (1)(1/0.02)(2)=100. I think if you plugged this into any scientific calculator, such as the Google calculator, as expressed, that's the result you'll get.
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@Michael Mendrin – But you're supposed to get 1000.
Additionally, I think that the multiplication sign would be needed.
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@Calvin Lin – Yes, I'm supposed to get 1000, not 100, and I did this like 3 am in the morning. Scratch that. I woke up because my arm went to sleep. Does that make any sense?
Hm, how about ( 1 + 2 + 3 + 4 ) ÷ % ?
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You need a number before the percentage sign isn't it?
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Dunno......
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@Calvin Lin – To clear doubts, I've added the clarifications in my details and assumptions. To be honest, this is the first time I've seen a percentage sign without a number in front of it.
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You must keep the digits in order
( 1 % ) − 2 × 3 ÷ 4