Lori has 18 stamps . She shows the stamps on pages of an album and groups of either 3, 6 or nine . How many different ways can she display the 18 stamps?

Question

The answer is 7 , but how do you arrive at the answer?

Answer 1

Think about how many ways you can get to 18 using the numbers given:. The first number is the number of groups and the second is the number in each group, which must be 3, 6, or 9 

 

1) 6 x 3  = 18

2) 3 x 6 = 18

3) 2 x 9 = 18

4) 2 x 3 + 2 x 6 = 18

5) 3 x 3 + 1 x 9 = 18

6) 1 x 3 + 1 x 6 + 1 x 9 = 18

 

There is one more. I'll bet you can figure it out!!!

Answer 2

 

 

3 x 6

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

6 groups of 3   <--- 1 

3 groups of 6   <--- 2

 

2 x 9

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

2 groups of 9   <--- 3

9 groups of pairs  <---- 4

 

6 + 12

 

--------

3 pairs and 3 quartets  =  3 x 2 + 3 x 4    <----- 5 

2 triplets and 3 quartets = 2 x 3 + 3 x 4   <-----6

 

3+15

--------

 

 3 quintuples and a triplet   = 3 x 5 + 3     <--- 7

 

There may be more....