Question 37267: A board game for 2 to 6 players has a deck of cards that can always be divided evenly among all the players. What is the smallest numbers of cards that are possible?
Found 2 solutions by checkley71, AnlytcPhil:
Answer by checkley71(8403)   (Show Source):
You can put this solution on YOUR website! THIS IS AN LCD (LOWEST COMMOM DENOMINATOR) PROBLEM
FACTORS OF 6 ARE 2*3 FACTORS OR 5 ARE 1*5 FACTORS OF 4 ARE 2*2 FACTORS OF 3
ARE 1*3 & FACTORS OF 2 ARE 1*2 THUS THE UNIQUE MULTIPLIERS ARE 2*3*5*2
WHICH =60 CARDS WHICH ARE DIVISABLE EVENLY BY 2,3,4,5,& 6
Answer by AnlytcPhil(1807)  (Show Source):
You can put this solution on YOUR website! A board game for 2 to 6 players has a deck of cards that can always
be divided evenly among all the players. What is the smallest numbers
of cards that are possible?
It's the LCM of 2,3,4,5,and 6
Start by listing them in a row with a vertical line on the left
| 2 3 4 5 6
|
|
Think of a prime number that will divide evenly into 2 or more of these.
Pick prime number 2, write it to the left of the vertical line:
2 | 2 3 4 5 6
|
|
Divide 2 into each number that 2 will divide evenly into and put what
you get underneath. Bring the other numbers down:
2 | 2 3 4 5 6
| 1 3 2 5 3
|
Think of a prime number that will divide evenly into 2 or more of these
on the bottom line. Pick prime number 3, write it to the left of the
vertical line:
2 | 2 3 4 5 6
3 | 1 3 2 5 3
|
Divide 3 into each number that 3 will divide evenly into and put what
you get underneath. Bring the other numbers down:
2 | 2 3 4 5 6
3 | 1 3 2 5 3
| 1 1 2 5 1
There is no prime that will divide evenly into two of the numbers
on the bottom line. So we multiply down the left side and across the
bottom
2 = 60
We would need 60 cards
Edwin
AnlytcPhil@aol.com
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