Brain Teasers
4+4+4+4=1?
Just using addition, subtraction, multiplication, and division, can you form all the numbers from 1 to 10 using exactly four 4's?
You may use parentheses and you can also combine fours to make other numbers (like 44 or 444).
You may use parentheses and you can also combine fours to make other numbers (like 44 or 444).
Hint
It may be helpful to know that you can make 0 with 4-4 and 1 with 4/4.Answer
(4+4)/(4+4) = 1(4x4)/(4+4) = 2
(4+4+4)/4 = 3
4+(4-4)/4 = 4
(4x4+4)/4 = 5
4+(4+4)/4 = 6
44/4-4 = 7
4+4+4-4 = 8
4+4+4/4 = 9
(44-4)/4 = 10
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Comments
4+(4-4)/4 = 4
I think if you do the brackets (BODMAS) first 4-4 = 0
then 4/4 will equal 1 and not 4.
I could have it wrong but I think that that is the answer.
Cheers
I think if you do the brackets (BODMAS) first 4-4 = 0
then 4/4 will equal 1 and not 4.
I could have it wrong but I think that that is the answer.
Cheers
I enjoyed try to slove it. Great!
But you need to do the 1/4 part first in 4 + 1/4. Thanks for pointing it out and thank you to luvupurple too.
I greatly enjoyed this teaser. This is, of course, part of Calculus! The fact that any integer can be made with four '4's is an interesting one isn't it? If you enjoyed this teaser, I would recommend a book to you which talks about math puzzles similar to this one. It is called "The Man Who Counted" by Malba Tahan, and is a very good read, combining mathematical puzzles and issues with a story of a Persian mathematician. I will reiterate - I really enjoyed this teaser!
thanks, This is personally one of my favourite teasers too! I'll go to the library soon to see if it's there. Thanks again!
You can make 7 without using 44:
4+4-4/4 = 7
4+4-4/4 = 7
If you allow other mathematical operators such as logarithms and square root signs, there is a general solution to the four 4s problem. That is you can write an expression for any integer whatsoever using just four 4's.
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