Can you solve it in your mind within 2 minutes - Tricky House Numbers Puzzle
video description
At first I solved this problem by trial and error, as the house numbers are reverse of each other, they must be two digits atleast. And since their difference ends with 2, I got the answer 19 and 91 within 5 secs. But later I thought of solving it with a different approach, -proving that 19 and 91 are the least possible values-
Comsider digit at tens place be x and unit place be y.
Then, original number =10x+y
Then, reversed number =10y+x.
Now, 10x+y - (10y+x) = z+2 (given the difference of the digits is 2, z>=0)
=> 9x-9y = z+2
=> x-y = (z+2)/9
Now, since x and y are integers, z+2 must be divisible by 9. Now, smallest number divisible by 9 which ends with 2 is 72.
So, 72/9 =8.
Since x and y are single digit numbers, they must lie between 1-9. But only 9-1 =8.
Hence, x= 9 and y=1.
So, the numbers are 19 and 91.
Date: 2023-11-15
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Comments and reviews: 20
Devon
let my house number = 10 a + b, then my friend's house number is 10 b+ a.
The difference is (10 a + b) - (10 b - a ) = some number which ends with 2 which and be expressed as 10 c + 2
so 9 a - 9 b = 10 c + 2 or 9 (a - b)= 10 c + 2 or a - b = 10 c + 2 / 9. A number which ends with 2 that is divisible by 9 is 72 and 72 divided by 9= 8 (in this case c is 7)
a - b = 8 means that -a- is 8 greater than b, so if a = 8, then b= 0 and if a = 1, then b= 9, so 08 and 80 (if b=0)
and 19 and 91 (if b=1. The difference between 80 and 8 =72 and the difference between 19 and 91 = 72 or ends with 2. Since I don't think you are considering 08 and 80 because 8 is written as 8 not 08, the answer is 19 and 91. Answer 19 and 91
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let my house number = 10 a + b, then my friend's house number is 10 b+ a.
The difference is (10 a + b) - (10 b - a ) = some number which ends with 2 which and be expressed as 10 c + 2
so 9 a - 9 b = 10 c + 2 or 9 (a - b)= 10 c + 2 or a - b = 10 c + 2 / 9. A number which ends with 2 that is divisible by 9 is 72 and 72 divided by 9= 8 (in this case c is 7)
a - b = 8 means that -a- is 8 greater than b, so if a = 8, then b= 0 and if a = 1, then b= 9, so 08 and 80 (if b=0)
and 19 and 91 (if b=1. The difference between 80 and 8 =72 and the difference between 19 and 91 = 72 or ends with 2. Since I don't think you are considering 08 and 80 because 8 is written as 8 not 08, the answer is 19 and 91. Answer 19 and 91
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LatiusAuro
I solved it in about 90 seconds, and here's how I did it:
Consider the houses as being XY and YX - this means the first house has a house number of (10-X)+Y, and both X and Y are swapped for the other. Here, 10>X>Y>0.
Next, subtract the second house number from the first, and you get a difference D equal to 9X-9Y.
As both 9X and 9Y are multiples of 9, this means D must also be a multiple of 9. The smallest D which ends in a 2 in this case is 72.
Plugging that in and dividing both sides by 9 gives you X-Y=8.
As X and Y are single digit numbers greater than 0, the only possible solution is X=9 and Y=1, giving the house numbers of 19 and 91.
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I solved it in about 90 seconds, and here's how I did it:
Consider the houses as being XY and YX - this means the first house has a house number of (10-X)+Y, and both X and Y are swapped for the other. Here, 10>X>Y>0.
Next, subtract the second house number from the first, and you get a difference D equal to 9X-9Y.
As both 9X and 9Y are multiples of 9, this means D must also be a multiple of 9. The smallest D which ends in a 2 in this case is 72.
Plugging that in and dividing both sides by 9 gives you X-Y=8.
As X and Y are single digit numbers greater than 0, the only possible solution is X=9 and Y=1, giving the house numbers of 19 and 91.
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Amit
I took less than one min because I know the fact that if we subtract a number by its reverse, the result will always be divisible by 9.
Also, the difference between both the digits on a 2 digit number X by 9 becomes the difference.
Now the lowest number divided by 9 which has 2 at digits place is 72. And which means the difference between two of its digits will be 8.
Now you can get all those numbers by keeping 72 in difference.
Like.
08 and 80
19 and 91
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I took less than one min because I know the fact that if we subtract a number by its reverse, the result will always be divisible by 9.
Also, the difference between both the digits on a 2 digit number X by 9 becomes the difference.
Now the lowest number divided by 9 which has 2 at digits place is 72. And which means the difference between two of its digits will be 8.
Now you can get all those numbers by keeping 72 in difference.
Like.
08 and 80
19 and 91
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raj
CHECK THIS OUT
difference between a number and a reversal will always be multiple of nine.
since we need difference ending with 2 find which is multiple of nine ending with 2 ie 72.
next step find the house number (minimum)
cant get difference 72 with single digits.
next with 2 digits AB and BA ie 10A + B and 10 B+ A.
Their difference will be 9(A-B) =72.
So A-B=8 which will give you 08&80, 71&17, 62&26.
like this if it is easy.
reply
CHECK THIS OUT
difference between a number and a reversal will always be multiple of nine.
since we need difference ending with 2 find which is multiple of nine ending with 2 ie 72.
next step find the house number (minimum)
cant get difference 72 with single digits.
next with 2 digits AB and BA ie 10A + B and 10 B+ A.
Their difference will be 9(A-B) =72.
So A-B=8 which will give you 08&80, 71&17, 62&26.
like this if it is easy.
reply
Jdnof
let 1st number be 10x + y
let 2nd number be 10y + x
1st - 2nd = 9x - 9y
9x - 9y should be 10k + 2 where k is a single-digit positive integer
9x - 9y = 9k + k + 2
9x - 9y - 9k = k + 2
x - y - k = (k + 2)/9
k must be 7 since x - y - k is an integer
x - y - 7 = 9/9
therefore x must be 9, y must be 1
the 2 numbers are 19 & 91
took me 90 secs in my head
good puzzle, thanks!
reply
let 1st number be 10x + y
let 2nd number be 10y + x
1st - 2nd = 9x - 9y
9x - 9y should be 10k + 2 where k is a single-digit positive integer
9x - 9y = 9k + k + 2
9x - 9y - 9k = k + 2
x - y - k = (k + 2)/9
k must be 7 since x - y - k is an integer
x - y - 7 = 9/9
therefore x must be 9, y must be 1
the 2 numbers are 19 & 91
took me 90 secs in my head
good puzzle, thanks!
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David
less than 1 minute. I just tried 12, 21, then 13, 31, then 14, 41. (notice the difference is decreasing by 1 each time from 9, to 8, to 7. 5 more to get to 2 so 14+5 = 19 so 19, 91 is the solution. However, since they are asking for the lowest pair of numbers that satisfy this, 19, 91 can be argued as wrong. What about -19 and -91? Who said house numbers have to be non-negative?
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less than 1 minute. I just tried 12, 21, then 13, 31, then 14, 41. (notice the difference is decreasing by 1 each time from 9, to 8, to 7. 5 more to get to 2 so 14+5 = 19 so 19, 91 is the solution. However, since they are asking for the lowest pair of numbers that satisfy this, 19, 91 can be argued as wrong. What about -19 and -91? Who said house numbers have to be non-negative?
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----
you are dumb and produce yourself that you know everything but you should not know everything and it is really that no one know everything it is possible to write houses numbers starting by any zero because of the country system that print the plates
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you are dumb and produce yourself that you know everything but you should not know everything and it is really that no one know everything it is possible to write houses numbers starting by any zero because of the country system that print the plates
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Cipher
I first realised the the lowest number that had a difference of two digits was 13 and 31 and then I just brute forced my way from there. 31-13, 41-14, 51-15 until I got up to 19. I didn't time myself but it felt like less than two minutes
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I first realised the the lowest number that had a difference of two digits was 13 and 31 and then I just brute forced my way from there. 31-13, 41-14, 51-15 until I got up to 19. I didn't time myself but it felt like less than two minutes
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disguisedhell
Your questions are getting easier and easier. I did this one in 5 seconds. Simply notice that the difference of a number and it's reverse is always divisible by 9. So, the lowest one must be 72. Please increase difficulty
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Your questions are getting easier and easier. I did this one in 5 seconds. Simply notice that the difference of a number and it's reverse is always divisible by 9. So, the lowest one must be 72. Please increase difficulty
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poiewhfopiewhf
Even though the same answer suits both possibilities the problem could have used more clarification about the -lowest house numbers- whether it meant the sum of them or just to get one of them as low as possible
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Even though the same answer suits both possibilities the problem could have used more clarification about the -lowest house numbers- whether it meant the sum of them or just to get one of them as low as possible
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lalit
#include-
using namespace std; -
int reverse(int k)-
--
int i=0; -
while(k)-
--
i=(i-10)+k%10; -
k/=10; -
--
return i; -
--
int main)-
--
int i, j; -
for(i=10; i
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#include-
using namespace std; -
int reverse(int k)-
--
int i=0; -
while(k)-
--
i=(i-10)+k%10; -
k/=10; -
--
return i; -
--
int main)-
--
int i, j; -
for(i=10; i
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Rahim
I solved it very simply. The house number should not 1 to 9 because there is no reverse for that number so I started differencing the number from 11 and I got at 19 and 91 the difference is 72
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I solved it very simply. The house number should not 1 to 9 because there is no reverse for that number so I started differencing the number from 11 and I got at 19 and 91 the difference is 72
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Dan
ab - ba = 10(a-b) -(a-b) = 9(a-b) and the only (a-b) to end in 2 when multiplied by 9 is 8 and the only pair (a, b) to do that is (9, 1. So a = 9, b = 1 and 91 - 19 = 72 ends in 2.
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ab - ba = 10(a-b) -(a-b) = 9(a-b) and the only (a-b) to end in 2 when multiplied by 9 is 8 and the only pair (a, b) to do that is (9, 1. So a = 9, b = 1 and 91 - 19 = 72 ends in 2.
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Shivam
I did it in less than 30 sec. But I had not thought of the case with digit 0, so if the logic for considering 08 and 80 as house nos. was correct then my answer was wrong.
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I did it in less than 30 sec. But I had not thought of the case with digit 0, so if the logic for considering 08 and 80 as house nos. was correct then my answer was wrong.
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Anthony
Wrong, the numbers are 13 and 31. The difference is -22. It ends with 2.
In order to be precise, you should state that the difference is a positive number.
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Wrong, the numbers are 13 and 31. The difference is -22. It ends with 2.
In order to be precise, you should state that the difference is a positive number.
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Arup
(10x+y)-(10y+x) = 9(x-y.
Now smallest multiple of 9 ending with is 72 =9(x-y.
So x-y =8. So 9-1 works the best
(since you normally don't see house#08)
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(10x+y)-(10y+x) = 9(x-y.
Now smallest multiple of 9 ending with is 72 =9(x-y.
So x-y =8. So 9-1 works the best
(since you normally don't see house#08)
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Omamba
You said lowest possible house number. Just because people don't normally start their house number with a '0' doesn't mean it isn't possible.
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You said lowest possible house number. Just because people don't normally start their house number with a '0' doesn't mean it isn't possible.
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Tylon
It never says you live at the reverse of your friend's house so you live in 80 they live in 8 you never said it works both ways
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It never says you live at the reverse of your friend's house so you live in 80 they live in 8 you never said it works both ways
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amod
Actually I misinterprete question. I thought that both house nos. ends with 2. in that case my ans was 2012 and 2102.
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Actually I misinterprete question. I thought that both house nos. ends with 2. in that case my ans was 2012 and 2102.
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Spartan
You are doing great brother. never stop! I did that in 2minutes. Challenge completed! Thank you
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You are doing great brother. never stop! I did that in 2minutes. Challenge completed! Thank you
reply
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