Okay, let's work this out... What we know: -32 stamps in all - rows (horizontal) - same # in each What we "want to know" : - # of combinations (different) Problem Solving : This is actually very easy its just the words than get ya! 1st : we need to figure out the factors of 32... In other words, we need to figure out _x_=32 and how many different combinations and ways there are! Note:(* means multiplication) #1: What are the factors of 32? 32: 1*32 , 2*16 , 4*8 32: 32*1 , 16*2 , 8*4 The factors (not including 1 are 2,4,8,16) Now, as you can see, there are 4 ways to get 32 as shown first. |||||||||||||||| |||||||||||||||| ^ That ¦ is 1 way with 16 in 2 rows. Basic multiplication, 16*2=32 or 16+16=32. But, this is also a way, || || || || || || || || || || || || || || || || Now there should be 2 in each row and 16 rows. Again 2*16=32 or 2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2=32 That's two ways so far. |||||||| |||||||| |||||||| |||||||| Another way which is 4 rows with 8 in each. 4*8=32 or 8+8+8+8=32 But, this is also a way, |||| |||| |||| |||| |||| |||| |||| |||| Now that is 8 rows with 4 in each. 8*4=32 or 4+4+4+4+4+4+4+4=32 That was our fourth way. Again NOT including 1. If you include 1 then there will be 6 ways but aside from that there are 4 ways. I hope that helped I worked hard typing this all for you. Any questions just ask!
