Find the number puzzle.

Ankita
Member • Dec 3, 2013

Find the number puzzle.

There is a number less than 3000 that when divided by 2 leaves a remainder of 1, when divided by 3 leaves a remainder of 2, when divided by 4 leaves a remainder of 3, When divided by 5 leaves a remainder of 4, when divided by 6 leaves a remainder of 5, and so on up to nine.

What is that number?
Please provide step by step solution to this problem.

Replies

Howdy guest!

Dear guest, you must be logged-in to participate on CrazyEngineers. We would love to have you as a member of our community. Consider creating an account or login.

Replies

kedarjk

Member • Dec 3, 2013

2519
I wrote a simple python program to find it out. 😉

Are you sure? This action cannot be undone.
Cancel
Ankita Katdare

Administrator • Dec 3, 2013

kedarjk
2519
I wrote a simple python program to find it out. 😉
Please share the script, friend! 😁

Are you sure? This action cannot be undone.
Cancel
kedarjk

Member • Dec 3, 2013

Its no brainer...
-----------------------------------------
for i in range (1,3000):
if i%9==8:
if i%8==7:
if i%7==6:
if i%6==5:
if i%5==4:
if i%4==3:
if i%3==2:
if i%2==1:
print "This is the number: "+ str(i)

-----------------------------------------

I was curious to check if there is really such number, so wrote a simple script. There must be some other logic to find it out.

Are you sure? This action cannot be undone.
Cancel
Anoop Kumar

Member • Dec 3, 2013

That's an bad programming, number of loops will be 2519.

This is class 8th problem which is calculated by following method, It's like following

LCM (reminders) *x - GCD(Numbers) until you find the solution. x is an Integer.

I don't remember that exact method.

Are you sure? This action cannot be undone.
Cancel
Alok mishra

Member • Dec 5, 2013

ianoop
That's an bad programming, number of loops will be 2519.

This is class 8th problem which is calculated by following method, It's like following

LCM (reminders) *x - GCD(Numbers) until you find the solution. x is an Integer.

I don't remember that exact method.
its n*LCM(divisor)-(difference Between divisor and remainder) , n is any natural number .

Are you sure? This action cannot be undone.
Cancel
Anoop Kumar

Member • Dec 5, 2013

Another example of this question is
find x such that
reminder is 2 when divided by 3,
3 when divided by 4,
1 when it's 5.

Are you sure? This action cannot be undone.
Cancel
smorgasbord

Member • Apr 23, 2014

Ankita Katdare
There is a number less than 3000 that when divided by 2 leaves a remainder of 1, when divided by 3 leaves a remainder of 2, when divided by 4 leaves a remainder of 3, When divided by 5 leaves a remainder of 4, when divided by 6 leaves a remainder of 5, and so on up to nine.

What is that number?
Please provide step by step solution to this problem.
A number when
divided by 2 leaves a remainder of 1 = divided by 2 leaves a remainder of 1
divided by 3 leaves a remainder of 2 = divided by 3 leaves a remainder of 1
divided by 4 leaves a remainder of 3 = divided by 4 leaves a remainder of 1
divided by 5 leaves a remainder of 4 = divided by 5 leaves a remainder of 1
.
.
.
. = divided by 9 leaves a remainder of 1

Which means we need LCM of 2,3,4,5 ( 60 ), 7 ( 420 ), 8 (420*2=840), 9 ( 840*3 ) = 2520 ... and something.

if we need all the right hand side of the ='s to be set right we need to add one to 2520, but we need all the left hand side of the ='s written above to be true, so need to subtract one from it.
2519.

Are you sure? This action cannot be undone.
Cancel
smorgasbord

Member • Apr 23, 2014

Hell! i made an egregious error:
A number when
divided by 2 leaves a remainder of 1 = divided by 2 leaves a remainder of -1
divided by 3 leaves a remainder of 2 = divided by 3 leaves a remainder of -1
divided by 4 leaves a remainder of 3 = divided by 4 leaves a remainder of -1
divided by 5 leaves a remainder of 4 = divided by 5 leaves a remainder of -1
.
.
.
. = divided by 9 leaves a remainder of -1

Which means we need LCM of 2,3,4,5 ( 60 ), 7 ( 420 ), 8 (420*2=840), 9 ( 840*3 ) = 2520, & -1 = 2519
sorry. 😛

Are you sure? This action cannot be undone.
Cancel