# Expert puzzle

gabe
what is 2+2?

ceptimus

Using the + symbol as a Logical OR, the answer is 2

In base 3 the answer is 11

In base 4 the answer is 10

In every other possible base, the 'normal' answer is 4

I'm sure there are many other possibilities...

TenaliRaman
G = {Z,+,*}
2 e Z
2+2 e Z
:p

The Bob
ceptimus said:

Using the + symbol as a Logical OR, the answer is 2

In base 3 the answer is 11

In base 4 the answer is 10

In every other possible base, the 'normal' answer is 4

I'm sure there are many other possibilities...

Base?

The Bob
I am going to say 2+2 is 2+2 as the question does not say 'what is the answer to 2+2?' or 'what does 2+2 equal?'

Ian Rumsey
The ? may indicate another digit, so it could read 2+21 or 2+22 etc, etc

gabe
man your stupid, 2+2=4 even a 5 year old would know that

K.J.Healey
then its not really an expert puzzle now is it?

Staff Emeritus
Gold Member
gabe said:
man your stupid, 2+2=4 even a 5 year old would know that

And you must be about 7 years old, because even an eight-year-old will know that the correct word to be used in your punctuation challenged "sentence" - the only puctuation used is the wrong one and you really should have three sentences there - is "you're", not "your" !

<Just a note that I'm aware of the 'conjunction rule' which is really archaic - in case you were planning on bringing that up.>

Good one, Goku. You say what I think.

The Bob
So what was the point in posting it gabe if you didn't want an unusual answer?

gabe said:
man your stupid, 2+2=4 even a 5 year old would know that

lol... trollism at its finest.

gabe
it was a joke! man that was funny :rofl:

ceptimus
The Bob said:
Base?

All your base are belong to us.

The Bob
ceptimus said:
All your base are belong to us.

Not getting it at all.

In Confusion

TenaliRaman
123 can be written as,
1*10^2 + 2*10 + 3
This representation as we know it is called the decimal representation.
Also this is called the *base 10* representation
cuz the number is written in the powers of 10.
In general a base 10 number can be written as,
a_n*10^n + ...+a_1*10+a_0
where 0<= a_i <=9 for all 0<=i<=n

As we can have base 10 representaion then we can have any base 'r' representation ...
A base r number can be represented as,
a_n*r^n + ...+a_1*r+a_0
where 0<= a_i <=r-1 for all 0<=i<=n

e.g "5 in base 10" is "101 in base 2"
note that : 1*2^2 + 0*2 + 1 = 5

Hope this helps.
-- AI

The Bob
TenaliRaman said:
e.g "5 in base 10" is "101 in base 2"
note that : 1*2^2 + 0*2 + 1 = 5

I think it will help and has but could you please write out the bases, above, and their equations, like at the top of your post.

So 5 in base 10 = 5
101 in base 2 = 5 because 1*2^1 + 0 + 1?

Sorry I am a pain but I have little understanding of this.

Thanks

ceptimus
In base 10 we have 10 different symbols: 0,1,2,3,4,5,6,7,8,9

In (say) base 4, we only have four symbols: 0,1,2,3

so counting in base 4 looks like this: 0,1,2,3,10,11,12,13,20,21,22,23,30...

The 'ultimate' low base is base 2 where only two symbols are used: 0,1

This base is used by computers as the 0 and 1 can be easily represented by the absence or presence of a voltage, or current, or charge etc. Because it is so widely used, Base 2 has a special name: Binary.

Counting in Base 2 (aka Binary) looks like this: 0,1,10,11,100,101,110,111,1000...

Hope that helps.

'All of your base are belong to us' is a cult-saying on the internet. It came from a video game. Try googling on it to find more, if you're interested.

The Bob
I GET IT. Man, I am slow.

Sorry guys, I took ages to get that.

Thanks TenaliRaman and Ceptimus. Appreciate the help.

check
In base 1 how would zero be expressed? Would one count like:
0,00,000,0000 etc
or no zero and do 1,11,111,1111 ?

The Bob
ceptimus said:
The 'ultimate' low base is base 2 where only two symbols are used: 0,1

check said:
In base 1

No base 1. Don't know why but not base 1.

nucleartear
May be the fingers are an excellent example of base 1!

TenaliRaman
base 2 is the "ultimate" limit only if one considers the schema/representation i proposed.

ppl have come up with many different representations which is in close analogy with this base representation

If u consider 0,1,2,3,4,5,6,... as just weighted symbols and that any base r representation as a representation which uses no more than abs(r) different symbols, then one can come up with many representations (Ofcourse all these representations need not have a bijection with the natural numbers).

So in view of this,
we can sort of have a base 1 representation, the counting in this schema would be
a,aa,aaa,aaaa,aaaaa,...
(One can use any symbol instead of a and assign it the weight 1)
This is called as a unary representation. (This is highly useful in many analysis of Turing machines)

One can even have negative bases as well (! Now u see why i wrote abs(r) in my earlier definition :) ).
A very nice base and the one used infrequently is the base -2 representation. The symbols used for this representations are 0 and 1 with their usual weights 0 and 1.
e.g,
1 = 1
0 = 0
11 = -1
10 = -2
100 = 4
101 = 5
110 = 2
and so on...

-- AI

The Bob
TenaliRaman said:
One can even have negative bases as well (! Now u see why i wrote abs(r) in my earlier definition :) ).
A very nice base and the one used infrequently is the base -2 representation. The symbols used for this representations are 0 and 1 with their usual weights 0 and 1.
e.g,
1 = 1
0 = 0
11 = -1
10 = -2
100 = 4
101 = 5
110 = 2
and so on...

-- AI

Erm... :uhh: am I the only one that doesn't understand this?

Sorry AI but I don't get it. Being slow again.

4newton
It depends on you profession.

If you are a mathematician you answer is 4

If you are an experimental physicist you will need to measure it.

If you are a theoretical physicist you will dream up some relative number.

If you are an account you will ask what do you want it to be.

TenaliRaman
Bob,
haven't got much time now ...
see if this helps,
abs(-2) = 2
so we can use two different symbols (say a and b and i will assign them values 0 and 1 but why not we use 0 and 1 themselves as symbols ... so we use 0 and 1 as symbols instead of a and b)

now 110 in base -2 ... so in base 10 it would be,
1*(-2)^2 + 1*(-2) + 0 = 2

so we see that 110 in base -2 is 2 in base 10

in this way numbers can be represented in base -2 ...

if any problems post again and i will try to detail things out...

-- AI

The Bob
TenaliRaman said:
Bob,
haven't got much time now ...
see if this helps,
abs(-2) = 2
so we can use two different symbols (say a and b and i will assign them values 0 and 1 but why not we use 0 and 1 themselves as symbols ... so we use 0 and 1 as symbols instead of a and b)

now 110 in base -2 ... so in base 10 it would be,
1*(-2)^2 + 1*(-2) + 0 = 2

so we see that 110 in base -2 is 2 in base 10

in this way numbers can be represented in base -2 ...

if any problems post again and i will try to detail things out...

-- AI

I believe I understand but I will have to do some in my own time and post again.

Cheers for the help :thumbs_up