\(\text{Diane has one 1-cent stamp, two identical 2-cent stamps, and so on, up to nine identical 9-cent stamps. In how many different arrangements can Diane paste exactly 10 cents worth of postage in a row across the top of an envelope? (Note, however, that simply rotating or inverting a stamp, or exchanging the positions of two stamps with the same denomination should be considered the same arrangement.) }\)

Guest Sep 7, 2019

#1**+1 **

**Here is my attempt at this. I come up with 16 combinations as follows:**

**1- 9 + 1 = 10 2 - 8 + 2 = 10 3 - 7 + 3 = 10 4 - 6 + 4 = 10 5 - 5 + 5 = 10 6 - 7 + 2 + 1 = 10 7 - 6 + 3 + 1 = 10 8 - 6 + 2 + 2 = 10 9 - 5 + 4 + 1 = 10 10 - 5 + 3 + 2 = 10 11 - 4 + 4 + 2 = 10 12 - 4 + 3 + 3 = 10 13 - 5 + 2 + 2 + 1 = 10 14 - 4 + 3 + 2 + 1 = 10 15 - 3 + 3 + 3 + 1 = 10 16 - 3 + 3 + 2 + 2 = 10**

Guest Sep 7, 2019

#4**0 **

Only one of your equations is equal to 10.

1- 9 + 1 = -7

2 - 8 + 2 = -4

3 - 7 + 3 = -1

4 - 6 + 4 = 2

5 - 5 + 5 = 5

6 - 7 + 2 + 1 = 2

7 - 6 + 3 + 1 = 5

8 - 6 + 2 + 2 = 6

9 - 5 + 4 + 1 = 9

**10 - 5 + 3 + 2 = 10**

11 - 4 + 4 + 2 = 13

12 - 4 + 3 + 3 = 14

13 - 5 + 2 + 2 + 1 = 13

14 - 4 + 3 + 2 + 1 = 16

15 - 3 + 3 + 3 + 1 = 19

16 - 3 + 3 + 2 + 2=20

Guest Sep 8, 2019