Twos and More Twos
You can express a number using only twos in following manner:(use 5 twos and any of the mathematical operators, plus exponents and parentheses)
1 = 2 + 2 - 2 - 2/2
5 = 2 + 2 + 2 - 2/2
7 = 22/2 -2 -2
and so forth.
Express the numbers 11 through 20 in this manner.
1 = 2 + 2 - 2 - 2/2
5 = 2 + 2 + 2 - 2/2
7 = 22/2 -2 -2
and so forth.
Express the numbers 11 through 20 in this manner.
posted by Zaux at
9:08 AM
13 Comments:
I came up with this solution:-
11= 2+2+2+2+2+2/2
12= 2+2+2+2+2+2
13= 2+2+2+2+2+2/2
14= 2+2+2+2+2+2+2
15= 2+2+2+2+2+2+2+2/2
16= 2+2+2+2+2+2+2+2
17= 2+2+2+2+2+2+2+2+2/2
18= 2+2+2+2+2+2+2+2+2
19= 2+2+2+2+2+2+2+2+2+2/2
20= 2+2+2+2+2+2+2+2+2+2
I then thought, this is too easy, I re-read the question, and went back to work.... Here are the easy solutions I have so far:-
11=
12= ((2x2)x2) - (2x2)
13=
14= ((2+2+2)*2)+2
15= ((2x2)x2) - (2/2)
16= ((2x2)x2)x (2/2)
17= ((2x2)x2) + (2/2)
18= (2x2) x (2x2)+2
19=
20= ((2x2)x2) + (2x2)
There are several ways of getting to the solutions above..
But it is Saturday night... I am out of here! The Big C can do without me tonight!
That hasn't posted as intended!
((2x2)x2) should be (2 x 2) squared for 12, 15, 16 & 17.
Gone.
I can't let it lie:-
11=
12= (2x2)² - (2x2)
13=
14= ((2+2+2)x2)+2
15= (2x2)² - (2/2)
16= (2x2)² x (2/2)
17= (2x2)² + (2/2)
18= (2x2) x (2x2)+2
19=
20= (2x2)² + (2x2)
11= (2+2/2)² + 2
Taxi not here yet.... 2 tins down, rest of the night to go.
19= 22-2-(2/2)
Taxi??????????
13= (22+2+2)/2
Yay!
Now... taxi - beer in fridge running dangerously low. Roland Emmerich will be filming this for his next world-ending cataclysmic film - more devastating than 2012!
11 = (2+2/2)² + 2
12 = (2x2)² - (2x2)
13 = (22+2+2)/2
14 = ((2+2+2)x2)+2
15 = (2x2)² - (2/2)
16 = (2x2)² x (2/2)
17 = (2x2)² + (2/2)
18 = (2x2) x (2x2)+2
19 = 22-2-(2/2)
20 = (2x2)² + (2x2)
Nice job Karl ... have a brew!
Hi Zaux. Is there a proper answer for 13 and 19? I've not found one :(
Chris...for 13, I have (22+2+2)/2 ...
for 19, I have 22-2-(2/2)
22 doesn't meet the criteria that you gave. I assumed that you were holding onto a proper answer for a while.
...oops, I've just noticed that you have allowed 22 in your examples, sorry.
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22/2+2-2
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