My twin lives at the reverse of my house number. The difference between our house numbers ends in two. What are the lowest possible numbers of our house?
My twin lives at the reverse of my house number. The difference between our house numbers ends in two. What are the lowest possible numbers of our house?
The circuit breaker box in your new house is in an inconvenient corner of your basement. To your chagrin, you discover none of the 100 circuit breakers are labeled, and you face the daunting prospect of matching each circuit breaker to its respective light. (Suppose that each circuit breaker maps to only one light.)
To start with, you switch all 100 lights in the house to “on,” and then you head down to your basement to begin the onerous mapping process. On every trip to your basement, you can switch any number of circuit breakers on or off. You can then roam the hallways of your mansion to discover which lights are on and which are off.
What is the minimum number of trips you need to make to the basement to map every circuit breaker to every light?
Last edited by doodlesmom on Tue, Oct 13 2020, 8:02 pm; edited 1 time in total
My twin lives at the reverse of my house number. The difference between our house numbers ends in two. What are the lowest possible numbers of our house?
The circuit breaker box in your new house is in an inconvenient corner of your basement. To your chagrin, you discover none of the 100 circuit breakers are labeled, and you face the daunting prospect of matching each circuit breaker to its respective light. (Suppose that each circuit breaker maps to only one light.)
To start with, you switch all 100 lights in the house to “on,” and then you head down to your basement to begin the onerous mapping process. On every trip to your basement, you can switch any number of circuit breakers on or off. You can then roam the hallways of your mansion to discover which lights are on and which are off.
What’s the question?
I’m waiting in the basement to hear your question.
Last edited by ExtraCredit on Tue, Oct 13 2020, 8:02 pm; edited 1 time in total
The circuit breaker box in your new house is in an inconvenient corner of your basement. To your chagrin, you discover none of the 100 circuit breakers are labeled, and you face the daunting prospect of matching each circuit breaker to its respective light. (Suppose that each circuit breaker maps to only one light.)
To start with, you switch all 100 lights in the house to “on,” and then you head down to your basement to begin the onerous mapping process. On every trip to your basement, you can switch any number of circuit breakers on or off. You can then roam the hallways of your mansion to discover which lights are on and which are off.
What is the minimum number of trips you need to make to the basement to map every circuit breaker to every light?
Hidden:
51. First time he closes 50 and goes up and takes note. Then every time he goes down he opens one and closes one.
The circuit breaker box in your new house is in an inconvenient corner of your basement. To your chagrin, you discover none of the 100 circuit breakers are labeled, and you face the daunting prospect of matching each circuit breaker to its respective light. (Suppose that each circuit breaker maps to only one light.)
To start with, you switch all 100 lights in the house to “on,” and then you head down to your basement to begin the onerous mapping process. On every trip to your basement, you can switch any number of circuit breakers on or off. You can then roam the hallways of your mansion to discover which lights are on and which are off.
What is the minimum number of trips you need to make to the basement to map every circuit breaker to every light?
That's a bit similar to the key hidden in the chessboard riddle.
I need
Hidden:
7 trips.
I assign to every circuit breaker a binary number from 1 to 1100100 (which would be 1 to 100 in decimal)
So 1 would be 1, 2 would be 10, 3 would be 11, 4 would be 100, 5 would be 101, etc.
Then I assign a number from 1 to 100 to every light, in the order where I pass them on my trip through the house, and I make list on my pad where I write down the numbers of all the lights in decimal writing, and make sure I don't mix them up. Next to each decimal number for a light, I leave 7 columns or spaces...
Then I first light up all the circuit breakers that have a 1 in the end, I.e. all odd numbers.
I go through the house, if the light is on, I note 1, if it is off, I note 0 in the last (most right) column
Then I light up all the circuit breakers that have a 1 in the penultimate position, I.e. 2 (10),3 (11),6(110), 7 (111), 10(1010), 11 (1011), 14 (1110), 15 (1111),
again I go through the house, and on my pad I assign a 1 to lights lit up and a 0 to lights not lit up...
I note the results in the penultimate column on my list from right to left...
then I light up all the circuit breakers that have a 1 in the third-to last position, that would be 4, 5, 6, 7, 12, 13, 14, 15, 20, 21, 22, 23, 28, 29, 30, 31, 36, 37, 38, 39, etc...
and so forth, till the seventh position...
And the 0 and 1 I wrote down in the seven columns for each lamp on my list would be exactly the binary number assigned to its circuit breaker...
Last edited by ChanieMommy on Wed, Oct 14 2020, 1:59 am; edited 4 times in total
I have a riddle that is the same as the circuit breaker riddle, but easier to visualise.
I have a magic trick.
I ask you to think of a number between 1 and 100. (It really could be between 0 and 127, but we say 1 to 100, so as not to confuse you).
Then I give you a set of cards with numbers on them, and I ask you to check each card whether your number is on it and to give me back only the cards with the number on them.
Now I can tell you which number you chose, and then I will ask you to give me back the remaining cards...
How do I have to make those cards? (which numbers should be written on each card?)
How many cards do I need?
How can I tell the number you thought of?
The answer to the second question is the answer to the circuit breaker riddle...
