Saturday, July 21, 2007

Four 3's

Using arithmetic combinations of four 3's express the integers from 1 to 15.
You must use all four 3's for each integer.
You may combine the 3's using the arithmetic operations +, -, * (multiplication) and / (division).
You are also allowed to use sqrt (square root) (e.g. sqrt(3) ).
You are allowed to use concatenation (e.g. 33 is valid as part of an answer).
You are allowed to use factorials. For example, 3! (or factorial(3)) = 3*2*1 = 6. (The factorial of an integer x! is the product of all the positive integers less than or equal to x).
You do not need to use anything other than those listed above - so no decimal places, powers of 3, trig operations, logarithms, cube/quartic/etc. roots, etc.

4 Comments:

Anonymous Joseph said...

1 = 33/33
2 = (3!)/((3*3)/3)
3 = (3*(sqrt(3)*sqrt(3)))/3
4 = ((3*3)+3)/3
5 = (3+3) - (3/3)
6 = 3+3+3-3
7 = (3+3) + (3/3)
8 = (3! + 3) - (3/3)
9 = 3 + 3 + (3^2/3)
10 = (3! + 3) + (3/3)
11 = 3! + 3! - (3/3)
12 = 3 + 3 + 3 + 3
13 = 3! + 3! + (3/3)
14 = (33/3) + 3
15 = (3*3) + 3 + 3

July 21, 2007 at 5:46 AM  
Blogger steven said...

All ok except you don't need to use the 2 in 3^2 for 9....

9 = 3 + 3 + (sqrt(3)*sqrt(3) ) works!

or 9 = (3 * 3) + (3 - 3) ...

July 23, 2007 at 7:37 AM  
Anonymous Anonymous said...

just do (3! + 3)+3-3

September 9, 2016 at 2:44 PM  
Anonymous Anonymous said...

what does sqrt mean?

September 20, 2016 at 6:06 PM  

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