Algebra

[msgail06]

While traveling, you meet a man with a task for you: " Take a certain amount of diamonds out of this bag of 500. This number, when divided by any natural number 2 through 7, always generates a whole number if you take away 1 diamond before dividing. Bring me this number and they are all yours"

You reach in... and pull out a number of diamonds, but doesnt produce a whole number when you take away one diamond then divide by 4. This number meets the other conditions from the problem.

2pt: How many diamonds do you have to pull to get all the diamonds
2pt: How many diamonds did you pull out?

 

[arthur ohlsten]

mod=modulo


let N be the number of diamonds, less than 500
N-1= mod 2,mod3,mod5,mod6,mod7
N-1=mod5,mod6,mod7
N-1=5[6][7]
N-1=210 or 420
N=211 or 421
=========================================================================
N-1=mod4,mod5,mod6,mod7
N-1=840
no value less than 500 satisfies the problem

Arthur

 

[soroban]

Hello, msgail06!

While traveling, you meet a man with a task for you:
"Take a certain amount of diamonds out of this bag of 500.
This number, when divided by any natural number 2 through 7, always generates a whole number,
if you take away 1 diamond before dividing.
Bring me this number and they are all yours"

You reach in and pull out a number of diamonds,
but doesnt produce a whole number when you take away one diamond then divide by 4.
This number meets the other conditions from the problem.

(a) How many diamonds do you have to pull to get all the diamonds?
(b) How many diamonds did you pull out?

\(\displaystyle \text{The factorization of the integers 2 to 7 is: }\:2,\;3,\;2^2,\;5,\;2\!\cdot\!3,\,7\)

\(\displaystyle \text{Their LCM is: }\:2^2\!\cdot\!3\!\cdot\!5\!\cdot\!7 \:=\:420\)

\(\displaystyle \text{(a) The required number of diamonds is: }\;421\)


\(\displaystyle \text{Your number failed when dividing by 4.}\)

\(\displaystyle \text{It was missing the }2^2\text{ factor.}\)

\(\displaystyle \text{(b) Your number was: }\2\cdot3\cdot5\cdot7) + 1 \:=\:211\)

 

[mmm4444bot]

How many diamonds do you have to pull to get all the diamonds 500

How many diamonds did you pull out? All of them, if you're smart and can run fast

 

[msgail06]

Thanks for the help guys!