I have no idea what binary numbers are. Wasn't taught in my school. That's why I couldn't get the answer to the chessboard riddle.
It's when you have just 2 diffrent digits, 0 and1, and you have to express every number with 0 and 1
That's exactly what you do with this game...
if the number is on the card, it's a one, if it's not on the card, it's a zero...
So then you would write down whther your number is on the differnt cards, starting with card 1 on the right and going on with cards, 2, 3, etc. to the left...
1 is 1 (0r 0000001)
2 is 10 (or 0000010)
3 is 11 (or 0000011)
4 is 100 (or 0000100)
5 is 101
6 is 110
7 is 111
8 is 1000
9 is 1001
10 is 1010
96 is 1100000
(because you would find 96 just on card nr. 6 and 7)
100 is 1100100 (because you would find 100 on cards3, 6 and 7, starting with 4, 32 and 64)
It's when you have just 2 diffrent digits, 0 and1, and you have to express every number with 0 and 1
That's exactly what you do with this game...
if the number is on the card, it's a one, if it's not on the card, it's a zero...
So then you would write down whther your number is on the differnt cards, starting with card 1 on the right and going on with cards, 2, 3, etc. to the left...
1 is 1 (0r 0000001)
2 is 10 (or 0000010)
3 is 11 (or 0000011)
4 is 100 (or 0000100)
5 is 101
6 is 110
7 is 111
8 is 1000
9 is 1001
10 is 1010
96 is 1100000
(because you would find 96 just on card nr. 6 and 7)
100 is 1100100 (because you would find 100 on cards3, 6 and 7, starting with 4, 32 and 64)
Okay......so binary numbers between 128 and 256 will be represented by 8 digits, correct?
So back to the circuit breaker riddle... If you had the good fortune that they were arranged in neat rows of 8 under each other I.e. 8 columns , 13 rows, you could do this:
Number them from 0 to 99 in binary
Then switch on every second column (skip the first, switch on the second, etc..) Those are the odd numbers, like card 1 in our magic trick
Note which lights are on.(1 for on, 0 for off, last digit of your 7 digit number)
then switch two columns to off, the next two to on, etc... This would be card 2, (start with 2, switch 2 on, 2 off) Go through house, note results.
Then switch off four columns, four columns on - that's card 3, starting with 4...
Then switch off the first row, swtich the seond row on, the third row off, fourth on, etc... that's card 4, starting with 8
Then switch rows 1 and 2 to off, 3 & 4 to on, 5&6 to off, etc. that's card 5, starting with 16
Then switch rows 1-4 to off, 5-8 to on, 9-12 to off, 13 to on...that's card 6, starting with 32
Then switch rows 1-8 to off, 9-13 to on, that's card 7, starting with 64
And that's the basis of the chessboard riddle but there is more to it
So back to the circuit breaker riddle... If you had the good fortune that they were arranged in neat rows of 8 under each other I.e. 8 columns , 13 rows, you could do this:
Number them from 0 to 99 in binary
Then switch on every second column (skip the first, switch on the second, etc..) Those are the odd numbers, like card 1 in our magic trick
Note which lights are on.(1 for on, 0 for off, last digit of your 7 digit number)
then switch two columns to off, the next two to on, etc... This would be card 2, (start with 2, switch 2 on, 2 off) Go through house, note results.
Then switch off four columns, four columns on - that's card 3, starting with 4...
Then switch off the first row, swtich the seond row on, the third row off, fourth on, etc... that's card 4, starting with 8
Then switch rows 1 and 2 to off, 3 & 4 to on, 5&6 to off, etc. that's card 5, starting with 16
Then switch rows 1-4 to off, 5-8 to on, 9-12 to off, 13 to on...that's card 6, starting with 32
Then switch rows 1-8 to off, 9-13 to on, that's card 7, starting with 64
And that's the basis of the chessboard riddle but there is more to it
Not knowledgeable of binary but, The following I was able to comprehend as well.
the way they did it was marking each breaker throughout with a 0 if you kept it closed and a 1 if it was open that round. And then going up to the light switches each time and marking with the same 0 if open and 1 if closed that round.
And then matching each switch with light.
Not knowledgeable of binary but, The following I was able to comprehend as well.
the way they did it was marking each breaker throughout with a 0 if you kept it closed and a 1 if it was open that round. And then going up to the light switches each time and marking with the same 0 if open and 1 if closed that round.
And then matching each switch with light.
This here is the same principle, but a bit more methodical... this way, you are sure, in a easy way, that you covered all circuit breakers and all lights in a minimum of effort...
And then you can note the binary number of the circuit breaker with each light, and the regular number of the light with each circuit breaker...
I just used this example to show a basic principle that also works for the key in chessboard riddle...
so: 0 to 1 (2 numbers - ) one digit
2-3: two digits
4-7; three digits...
And it always changes at powers of 2...
Binary works exactly the same way as our decimal system, except that there are 2 digits instead of 10. So in the rightmost place, you either have a zero or a 1. And instead of going up by a power of 10 in the next place, it goes up by a power of 2. So 11 means (1) 2 and (1) 1, making 3. You can represent any number in binary, and it’s much more simple and that’s why computers use it. Each place is just 2 choices. Like a switch. It’s either on or off. Which, by the way, is what is represented by the on/off buttons on all computers. It’s a 1 inside a zero. Fun fact.
There are 10 types of people in the world. Those who understand binary and those who don’t.
It looks like I missed some really great stuff. I’m going to have to go back and read all these riddles. I just didn’t have the time to focus on them today.
