Write the number 17 using exactly six ones, any or all of the operations are allowed. Parenthesis are allowed as well.

Question

Extremely stuck on this problem, and its the first day of school! Please help!

Answer 1

in the binary systerm with base 2

converting to decimal numbers

1=1=2^0

10=2=2^1

11=3

100=4=2^2=2x2

101=5

110=6

111=7

1000=8=2^3=2x2x2

1001=9

1010=10

1011=11

1100=12

1101=13

1110=14

1111=15

1111+1=16=2^4 = 2x2x2x2

1111+1+1 = 17 written with six ones

=10001=2^4+1 =2x2x2x2+1

or sticking to just decimal numbers

(1+1)^(1+1+1+1)+1=2^4+1=2x2x2x2+1= 16+1=17

but that's 7 ones

11+(1+1)(1+1+1) = 11+2(3)=17 but 7 ones again

maybe there's a way to do it with 6 ones, but so far I don't see it

a combination of decimal and binary:

11+(1+1)(3) = 17, just substitute 11 for 3 in binary, that's 6 ones

11+(1+1)(11 in binary) =17

go with the binary number system, base 2

I've heard Common Core actually teaches it as early as 5th grade these days.

(1+1)^(1+1+1+1)+1 (7 ones)

converts to 2^4+1 = 16+1 =17

Answer 2

(1+1)^(1+1+1+1) +1 = 2⁴ + 1 = 16 + 1 = 17 (Hoorah!)