SOLUTION: 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

Question 260146: 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?

Found 2 solutions by jim_thompson5910, richwmiller:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Hints:

Part 1) Simply find the LCM of 2, 3, 4, 5, 6, 7 and add one to that result.

Part 2) In this case, find the LCM of 2, 3, 5, 6, 7 and add one to that result.
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
4*3*5*7=420
420+1
I removed 2 and 6 because 4 and 3 deal with them.
421 is your number.

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