Maths- Gym for Brainiacs

No progress peeps? Hala2, if you give up I'll write the answer

Been busy for a while.

So, for the above question, you are looking to prove* xyz is divisible by 3 if x+y+z is divisible by 3 right?

Going by what you said, x+y+z=3a.

xyz = 100x + 10y + z

xyz = 100x + 10y + 3a - x - y

xyz = 99x + 9y + 3a

xyz = 3(33x + 3y + a)

xyz = 3*b, where b = 33x + 3y + a, which is another natural number.

Is that right?

I thought this thread would fail..but wow, 12 pages for a thread full of maths

Soul wrote:I thought this thread would fail..but wow, 12 pages for a thread full of maths

Enjoy Or better, ask and learn :lol!:

kiranr wrote:Been busy for a while.

So, for the above question, you are looking to prove* xyz is divisible by 3 if x+y+z is divisible by 3 right?

Going by what you said, x+y+z=3a.

xyz = 100x + 10y + z

xyz = 100x + 10y + 3a - x - y

xyz = 99x + 9y + 3a

xyz = 3(33x + 3y + a)

xyz = 3*b, where b = 33x + 3y + a, which is another natural number.

Is that right?

+1

Next question:

topic: numerical theory
difficulty: hard
requirements: junior high school


Find a 10-digit prime number which contains digits from 0-9. The number isn't allowed to start with 0 and each digit from 0 to 9 should be used once only.

Hint: a prime number is a number which is divisable by 1 and itself only. Examples: 1, 3, 5, 7, 11, 13...


Also, the answer is really short. Like I said, junior high level

It is not possible Babun with the given conditions.

Since you said each number from 0 - 9 should be used only once, adding up the numbers from 1 to 9, ignoring 0, you get 45 which is a multiple of 3.

Spot on, I wanted to introduce the other way. Sometimes, you need to prove the impossible to find the right answer

topic: basic Newtonian mechanics
difficulty: hard
requirements: junior high school

Goallegacy Gym Question

Franchise wanted to try out a new version of intervall training. He ran up and down on an escalator at 2 a.m. with constant velocity. To get his timing right he was counting the number of steps he mounted while running up and down. While mounting the escalator he counted a=24 steps, while descending b=264 steps.
The question: how many steps were visible on this escalator at any given moment?

Notice, I drew two escalators because I wanted to write numbers cleanly. There's only one escalator in question!

Have fun! :lol!:

the escalators move at the same rate right?

spanky489 wrote:the escalators move at the same rate right?

There's only one escalator. I drew two to make the question apparent. You know when an escalator moves only a certain numbers of its steps are visible on the outside. The question is, how many of them are visible at any point given?

Do you like this question more than numerical theory?

Immortal Babun wrote:

spanky489 wrote:the escalators move at the same rate right?

There's only one escalator. I drew two to make the question apparent. You know when an escalator moves only a certain numbers of its steps are visible on the outside. The question is, how many of them are visible at any point given?

Do you like this question more than numerical theory?

i love it if u had posted it on valentines day i think i would have dined with it

spanky, having trouble or not getting started yet?

I know Franchise's velocity is the number of steps visible at any point of time. But i can't figure out how to arrive at the solution.

kiranr wrote:
I know Franchise's velocity is the number of steps visible at any point of time. But i can't figure out how to arrive at the solution.

Wrong You need Franchise's and escalator's velocity in the end but their velocity aren't the number of visible steps

I managed to solve the question in 3 totally different ways The third one disregards Franchise totally but is more of a mathematical solution

One of my solutions was similar to ' Shorty Jack and Lanky Dani' question
Take it as a hint. I think there're multiple more ways to solve it

Immortal Babun wrote:One of my solutions was similar to ' Shorty Jack and Lanky Dani' question
Take it as a hint. I think there're multiple more ways to solve it

havent started yet been busy with school ill probably take a look at it right now after i do my chores.

is the answer 144 steps?

spanky489 wrote:is the answer 144 steps?

Wrong, post your way of solving
Where are you from by the way? Surely not Indian

Immortal Babun wrote:

spanky489 wrote:is the answer 144 steps?

Wrong, post your way of solving
Where are you from by the way? Surely not Indian

x+y=24
x-y=264
2x=288
x=144
from slovenia btw

spanky489 wrote:

Immortal Babun wrote:

spanky489 wrote:is the answer 144 steps?

Wrong, post your way of solving
Where are you from by the way? Surely not Indian

x+y=24
x-y=264
2x=288
x=144
from slovenia btw

Slovenian girls are
I was one time in Bratislava. The girls there look like models Wait, Bratislava is in Slovakia... :lol!: I don't have a clue about Slovenia then
To the question, how am I supposd to solve your mistery? First of all, what are x and y in your calculation?
My wild guess, you're trying to distinct Franchise's velocity and that of escalator but instead of using a term for velocity you're working with absolute number of steps. That's where your way fails
Your premise isn't bad for starters. You just need to modify it properly (red)

Immortal Babun wrote:

spanky489 wrote:

Immortal Babun wrote:

spanky489 wrote:is the answer 144 steps?

Wrong, post your way of solving
Where are you from by the way? Surely not Indian

x+y=24
x-y=264
2x=288
x=144
from slovenia btw

Slovenian girls are
I was one time in Bratislava. The girls there look like models

To the question, how am I supposd to solve your mistery? First of all, what are x and y in your calculation?
My wild guess, you're trying to distinct Franchise's velocity and that of escalator but instead of using a term for velocity you're working with absolute number of steps. That's where your way fails
Your premise isn't bad for starters. You just need to modify it properly (red)

bratislava=slovakia=/= slovenia

and the problem:
x and y are motion vectors where x is the velocity of the elevator and y is the velocity of the runner. the escalator is always in one direction but the runner changes directions hence the plus and minus.

spanky489 wrote:

Immortal Babun wrote:

spanky489 wrote:

Immortal Babun wrote:

spanky489 wrote:is the answer 144 steps?

Wrong, post your way of solving
Where are you from by the way? Surely not Indian

x+y=24
x-y=264
2x=288
x=144
from slovenia btw

Slovenian girls are
I was one time in Bratislava. The girls there look like models

To the question, how am I supposd to solve your mistery? First of all, what are x and y in your calculation?
My wild guess, you're trying to distinct Franchise's velocity and that of escalator but instead of using a term for velocity you're working with absolute number of steps. That's where your way fails
Your premise isn't bad for starters. You just need to modify it properly (red)

bratislava=slovakia=/= slovenia

and the problem:
x and y are motion vectors where x is the velocity of the elevator and y is the velocity of the runner. the escalator is always in one direction but the runner changes directions hence the plus and minus.

You missed my edit I wrote that Slovenia =|= Slovakia
You started off right but how could velocity equal to steps? :lol!:

(Vf + Ve)T(u) = X

(Vf - Ve)T(d) = X

And

11*(Vf - Ve) = Vf + Ve

Dont know how to proceed further.

T(u) - time taken to climb up and T(d) - time taken to climb down.

X is the length of the elevator.

kiranr wrote:(Vf + Ve)T(u) = X

(Vf - Ve)T(d) = X

And

11*(Vf - Ve) = Vf + Ve

Dont know how to proceed further.

T(u) - time taken to climb up and T(d) - time taken to climb down.

X is the length of the elevator.

Very interesting arrangment. You're a lot closer to the solution than you think As for Ve , there's an easy way to substitute it with a number
Don't forget that 24 and 264 are given for a reason. Your way resembles my first solution

Immortal Babun wrote:

kiranr wrote:(Vf + Ve)T(u) = X

(Vf - Ve)T(d) = X

And

11*(Vf - Ve) = Vf + Ve

Dont know how to proceed further.

T(u) - time taken to climb up and T(d) - time taken to climb down.

X is the length of the elevator.

Very interesting arrangment. You're a lot closer to the solution than you think As for Ve , there's an easy way to substitute it with a number
Don't forget that 24 and 264 are given for a reason. Your way resembles my first solution

i got this as well but u have 2 different times, for X in that equation you put in 24 and 264.

spanky489 wrote:

Immortal Babun wrote:

kiranr wrote:(Vf + Ve)T(u) = X

(Vf - Ve)T(d) = X

And

11*(Vf - Ve) = Vf + Ve

Dont know how to proceed further.

T(u) - time taken to climb up and T(d) - time taken to climb down.

X is the length of the elevator.

Very interesting arrangment. You're a lot closer to the solution than you think As for Ve , there's an easy way to substitute it with a number
Don't forget that 24 and 264 are given for a reason. Your way resembles my first solution

i got this as well but u have 2 different times, for X in that equation you put in 24 and 264.

Wrong, X is the number of visible steps in his equation and it's the right way. He has to incorporate 24 and 264 in the left part. The idea of time units would help you guys further