Does it seem impossible to count?
2 2 2 = 2
Without touching the right side of the equation, can you find the number of ways you can make the equation true? You are only allowed to use fundamental operators like addition, subtraction, multiplication, division and parenthesis.
Details and assumptions :
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You must use parenthesis.
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You can use the parenthesis in in two ways, i.e. ( 2 + 2 ) − 2 = 2 and 2 + ( 2 − 2 ) = 2 are considered distinct.
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You can combine digits.
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BODMAS is applied.
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You are not allowed to use negative integers, i.e, ( − 2 × − 2 ) − 2 or − 2 × ( − 2 ) 2 is not allowed
The answer is 10.
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2 solutions
Moderator note:
Why are these the only ways?
Why can't I use two pairs of parenthesis?
What about ( − 2 ∗ − 2 ) − 2 , − 2 ∗ ( 2 / ( − 2 ) ) etc.? There are many many more like this, I gave up counting when I realised this. Counting the negatives also will take quite a long time, so I gave up and tried random answers.
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Thanks sir, I've edited the question accordingly.
What 2 pairs of parentheses can we use challenge master?
Good sol'n Sravanth! Done by this way.. Upvoted! ⌣ ¨
Proper way is to list + − × ÷ for (2 2) 2 of 6 among 16, and + − × ÷ for 2 (2 2) of 4 among another 16. 6 + 4 = 10. Considered distinct would be 10 or otherwise multiples of 10.
Answer: 1 0
Can you explain the sixth . It would be half .
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I don't think so. Using BODMAS, we must solve the brackets i.e, 2 2 × 2 = 1 × 2 = 2
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Yeah , sorry for it , I don't know what I was that time. Might have taken the seventh one in which the bracket is the first 2 . SORRY .
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@Karandeep Singh Ludhar – No need to say sorry, mistakes happen. ⌣ ¨
With two 2's we can make: (1) 2-2=0; (2) 2÷2=1; or (3) 2+2=2×2=4.
In case (1), 0+2=2+0=2-0=2 (1×3 ways).
In case (2), 1×2=2×1=2÷1=2 (1×3 ways).
In case (3), 4÷2=4-2=2 (2×2 ways).
In total, we have 10 ways.
1 . ( 2 + 2 ) − 2 = 2 2 . 2 + ( 2 − 2 ) = 2 3 . ( 2 + 2 ) ÷ 2 = 2 4 . ( 2 − 2 ) + 2 = 2 5 . 2 − ( 2 − 2 ) = 2 6 . ( 2 ÷ 2 ) × 2 = 2 7 . 2 ÷ ( 2 ÷ 2 ) = 2 8 . ( 2 × 2 ) − 2 = 2 9 . ( 2 × 2 ) ÷ 2 = 2 1 0 . 2 × ( 2 ÷ 2 ) = 2
Do you think these are the only possible ways? If not, submit the other possible ways.