Brain Teasers
Five Fives
5 5 5 5 5 = 37
Can you make a target number 37 by using five 5s?
You can use any math operator or group the 5s (as in 555)
There are at least two different ways.
Can you make a target number 37 by using five 5s?
You can use any math operator or group the 5s (as in 555)
There are at least two different ways.
Answer
Since the total of five 5s is 25, we have to choose an operator which can make a large number.Obviously, the multiplication operator is not good enough. We chose the factorial operator!
((5!+5!)-55)/5 = (120+120-55)/5 = 185/5 = 37
5!/(5+5)+5*5 = 120/10 + 25 = 12 + 25 = 37
A third solution uses "raising to the 5th power"
((5+5)/5)**5 + 5 = 37
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Comments
((5! + summation 5) / 5) + 5 + 5 =
((120 + 15) / 5) + 10 =
(135 / 5) + 10 = 27 + 10 = 37
((120 + 15) / 5) + 10 =
(135 / 5) + 10 = 27 + 10 = 37
yeah i did the third solution good teaser
Good teaser but answer was qite complicated
This is going to be difficult to write without mathematical symbols but:
[log (base (root(root(root(root(root5))))))5 + 5] *5/5
= [32 + 5 ]* 1
= 37
[log (base (root(root(root(root(root5))))))5 + 5] *5/5
= [32 + 5 ]* 1
= 37
I was bummed out when I first read the answer. You said at least two, so I figured I'd go until I found three before reading the answer. I found the same three as in your answer.
So I pulled out the multifactorial operators and came up with several more. The multifactorials are almost like cheating since you can get a very large collection of numbers that are multiples of 5 using a single 5, which of course means that with two fives you can get an even larger set of numbers. Hey, you said any mathematical operator
Here are but a few additional possibilities:
(5! - 5 - 5) / 5 + 5!!
= (120 - 5 - 5) / 5 + 15
= 110/5 + 15 = 22 + 15 = 37
(5! + 5! + 5! + 5!!!) / 5!!!
= (120 + 120 + 120 + 10) / 10
= 370/10 = 37
555 / (5!!! + 5)
= 555 / (10 + 5)
= 555/15 = 37
(5!!)!!!!!!!!!!!!! + 5 + (5 + 5)/5
= 15!!!!!!!!!!!!! + 5 + 10/5
= 30 + 5 + 2 = 37
(5!!/5) ^ (5!!/5) + 5!!!
= (15/5) ^ (15/5) + 10
= 3^3 + 10 = 27 + 10 = 37
(((5!!!)!!!!!!) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! / 5 + 5) ^ (5/5)
= ((10!!!!!!)!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! / 5 + 5) ^ 1
= (40!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! / 5 + 5) ^ 1
= (160 / 5 + 5) ^ 1
= (32 + 5) ^ 1 = 37^1 = 37
And my favorite:
((5!!!)!!! + 5!!! x 5!!! - 5!!!) / 5!!!
= (10!!! + 10 x 10 - 10) / 10
= (280 + 100 - 10) / 10
= 370/10 = 37
So I pulled out the multifactorial operators and came up with several more. The multifactorials are almost like cheating since you can get a very large collection of numbers that are multiples of 5 using a single 5, which of course means that with two fives you can get an even larger set of numbers. Hey, you said any mathematical operator
Here are but a few additional possibilities:
(5! - 5 - 5) / 5 + 5!!
= (120 - 5 - 5) / 5 + 15
= 110/5 + 15 = 22 + 15 = 37
(5! + 5! + 5! + 5!!!) / 5!!!
= (120 + 120 + 120 + 10) / 10
= 370/10 = 37
555 / (5!!! + 5)
= 555 / (10 + 5)
= 555/15 = 37
(5!!)!!!!!!!!!!!!! + 5 + (5 + 5)/5
= 15!!!!!!!!!!!!! + 5 + 10/5
= 30 + 5 + 2 = 37
(5!!/5) ^ (5!!/5) + 5!!!
= (15/5) ^ (15/5) + 10
= 3^3 + 10 = 27 + 10 = 37
(((5!!!)!!!!!!) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! / 5 + 5) ^ (5/5)
= ((10!!!!!!)!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! / 5 + 5) ^ 1
= (40!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! / 5 + 5) ^ 1
= (160 / 5 + 5) ^ 1
= (32 + 5) ^ 1 = 37^1 = 37
And my favorite:
((5!!!)!!! + 5!!! x 5!!! - 5!!!) / 5!!!
= (10!!! + 10 x 10 - 10) / 10
= (280 + 100 - 10) / 10
= 370/10 = 37
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