Using only the numbers 1, 3, 4, and 6, together with the operations +, −, ×, and ÷, and unlimited use of brackets, make the number 24. Each number must be used precisely once. Each operation may be used zero or more times. Decimal points are not allowed, nor is implicit use of base 10 by concatenating digits, as in 3 × (14 − 6).
As an example, one way to make 25 is: 4 × (6 + 1) − 3.
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Even though there's probably more, i got 6 answers. They are: 166/4, 4x6, 6x4, (4+6)x3-6, (3x6)+6, (4x13)-6x4-4. I'll keep looking for more, but so far i have 6
ReplyDeleteIris, although you have some good answers, each number can only be used ONCE.
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ReplyDeleteonce again i'm still searching, but with exponents i found 2. they are: 6/((1³)/4) and (4x6)x(1³)
ReplyDeleteI tryed to make 24 many ways.The closest I got was 23 and 26. So I do not think that this is very hard.(maybe I am just dum).
ReplyDelete$$$EM$$$
Do we have to use all the number?
ReplyDeleteI found nine ways to make 24. This is not using exponents, and not using some numbers. ( Some ways such as 4 x 6 and 6 x 4, might not count.)
ReplyDelete6 x 4
4 x 6
6 x 1 x 4
6 x 4 x 1
1 x 4 x 6
4 x 1 x 6
(1 + 3) x 6
6 / 1 x 4
4 / 1 x 6
yes, "you have to use each number precisely once"
ReplyDeleteOk so that means that we HAVE to use each number...or else it doesn't count? Sorry Iris I just want to make sure I get it!
ReplyDelete-KATTY-
yes, that is correct, and you cant add numbers together; 1, 4 turn into 14 (thats not allowed) though you can do 1, 4 = 1+4=5
ReplyDeleteok now I really can't figure it out...
ReplyDeletei found every way leo did so i dont really know what to say....
ReplyDeletems.d,
Does 6x4 and 4x6 count as two??
if it works can u do it backwards???
chris, it doesnt work because you have to use EVERY number (and only once)
ReplyDeleteLike Iris said there are a few ways with exponents.
ReplyDeleteIncluding:
(4 X 6) X (1 to the third power)
(6/1 to the third power) X 4
(4/ 1 to the third power) x 6
you have to use EVERY number in the equation, I think.
ReplyDeleteAll numbers need to be used in the equation.
ReplyDeleteNumbers can be in fraction form too!
ok well the only ones i have are: 6*4*1 to the power of 3, 4*6*1 to the power of 3, 6/1to the power of 3*4, 4/1 to the power of 3 *6, 1to the power of 3 6*4,1 to the power of 3 *4*6, 6/1to the power of3*4, 4/1to the power of 3 *6, 6*1 to the power of3*4, 4*1 to the power of 3*6, 4*6/1 to the power of 3, 6*4/1 to the power of 3, 4*(6/1 to the power of 3), 6*(4/1 to the power of 3), 4*(1 to the power of3*6), 6*(1 to the power of 3*), (6*4)*1to the power of 3, (4*6)*1to the power of3,(6*4)/1 to the power of 3,(4*6)/1 to the power of3, (6/1to the power of 3)*4,(4/1to the power of 3)*6, 6*1 to the power of 3*4, and the last one is (4*1 to the power of 3)*6. so i have 24.
ReplyDeletesorry that's all i could find
ReplyDeleteAdele, you last one equals 384. I think you have to write 4 X (1 to the power of 3) X 6.
ReplyDeletejust guessing
My answer is 6/(1-3/4). The way I thought of this answer is that since Ms.Dimitry said I could use fractions I just experimented and found the answer. The way you work this out is that first you do what is in the brackets so 1-3/4. That is 1/4. Next you do 6 / 1/4 which because of the law of dividing fractions is instead 6x4/1. 4/1 is 4 so 6x4=24. Thats my answer.
ReplyDeleteoh yeah, sorry i agree with leandro, i should of done that, ops sorry
ReplyDeleteThe two I figured out so far are 1 to the power of 3 x 4 x 6 and 6/((1 to the power of 3/4)). I figured these out by basically experimenting. I started using the obvious ones with exponents (1 to the power of 3 which = 1). (I'm not counting ones that switch the numbers around, I'm not sure if they count.)
ReplyDeleteThere is one answer that I found. First you solve what is in the brackets. (1 - 3 quarters = 1 quarter.) Next you multiply six by 1 quarter.(6 divided by 1 quarter = 24.) When you divide a number by a fraction, it is equivalent to multiplying the by that part of a whole. For example 6 divided by .20 = 30, or 6 X 5.
ReplyDelete(Ms. Dimitry, thanks for the hint about using fractions.)
Okay I have two more answers but I'm not sure if it's okay to use factorials. But I'm giving it a go. Anyways I was experimenting on my "scientific" calculator when I noticed the factorial sign. So here we are now. One that does is 6!/4! -3! x 1 = 24. Another one is 4! - 3! + 6 x 1 =24. I'm still looking for more!
ReplyDeleteI'm pretty sure I didn't get all of them but here's the last two I can find: 6/(1-3/4) = 24. And the last one is 6/1 to the power of 3/4. I figured these out by trial and error by using fractions and the knowledge of 6 x something. The first one is just a longer version of 6 divided by 1/4, because 3/4 = 3/4 and 1= 3/4 = 1/4 and then 6 divided by 1/4 =24. The second one was also based on the grounds of 6 divided by 1/4 = 24 because 1 to the power of 3 is still one so they are all similar in this way. If you went on you could probably find more on the basis of 6/ 1/4.
ReplyDeleteandrea, 6/(1-3/4) doesn't equal 24....
ReplyDeleteI saw many answers to help me solve this one but they were all # to the power of # and since I don't understand powering numbers or whatever it's called so I thought out one. (2x6) + (3x4) which equals 24.
ReplyDeletei found 4.......
ReplyDelete(1+3)x 6,
6 x 4,
6 x 1 x 4,
(6 x 2) + (4 x 3)
There are 2 that I found that nobody else found. the first is really simple: 6*3+2+4- I can't believe no one thought of it!The second is 6/3 (meaning 6 thirds)*4*2. This works because 6/3 also equals 3, and then 3*4=12, and 12*2=24.
ReplyDeleteMs. D I have no clue what an exponent is, or how to us it. That seems to be the only way to answer this problem.
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ReplyDeletei have another answer. its very innovative... so first you take the 6 and turn it 180 degrees so now it's a 9! from here i can make 9x3-4+1=24! lol
ReplyDeleteScarlett, look at using the numbers in fractions. Exponents are not the ONLY way to answer the question.
ReplyDeleteUmmmm. 1346......Thi is WAY late but i will try t do something..... So if you CAN use as many as you can....:
ReplyDelete6x4
(6 x 2)+(4x3)
(1 + 3)x 6
6x 1 x 4
4/1 x 6
6/1 x 4
1 x 4 x 6
4 / 1 x 6
I know nothing about exponents, can't use fractions properly, CAN use factorials but no well, cannot use powers either....
Well i think that is 8.... yes i believe so.... Yeah... well thats it.......
Ooops ummm. i meant CANNOT not CAN......
ReplyDeleteOh also this 6 / (1-3 (3/4)). That means i got 9!!!!!
ReplyDeleteoops i meant 6 / (1 - (3/4))
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ReplyDeletei got 9 theres probably more i just got kinda lazy Sorry? death to math
ReplyDeleteUm, I only got one way which equaled 24 but it's (4x6)x (1 to the third power)=24. Sorry i posted late i just couldnt find an answer. I think i was looking too hard. Some of the ways i found ot get close to 24 were: (6x3)+4+1=23, (6x4)+3-1=26 and (6x4)+1-3=22.
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