Math help!!!!!!?

Question

Okay...I need to answer this question, but I need to know why its the answer.
Joel goes to the post office to purchase four stamps. In how many ways can the clerk give him his purchase so that all four stamps are connected (assumng the stamps are squares)?

Answer 1

I think the first two answers are way too low. Think of a block of stamps:
12
34
then move one above 2:
1
2
34
then move 1 to the right of 2:
21
34
then move 1 down:
2
341
then move 1 below 4:
2
34
1
then put 1 under 3:
2
34
1
then put 1 to the left of 3:
2
134
So far I have 7 combos and I've only moved stamp 1 around.
I think there are 6 more possiblities if I move stamp 2 around the block, then 6 more if I move stamp three around the block, and 6 more if I move stamp 4 around the block, for a total of 25? I still thinking about it.

Answer 2

Here are the 19 ways you can arrange them:

If you can't make them out, try to paste them into notepad and use a proportional font, like the TERMINAL font.

horizontal:

OOOO

Revolve the last stamp around the first 3:

OOO
__O

OOO
_O

OOO
O

O
OOO

_O
OOO

__O
OOO

vertical:

O
O
O
O

Revolve the last stamp around the first 3:

OO
O
O


O
OO
O


O
O
OO

_O
_O
OO


_O
OO
_O

OO
_O
_O

from horizontal, Revolve the last 2 stamps around the first 2:

OO
_OO

OO
OO

_OO
OO

(next 2 positions will only repeat the 1st and 3rd, so we'll skip counting them)

next, from vertical, Revolve the last 2 stamps around the first 2:

_O
OO
O

(skip the square position - 2x2)

O
OO
_O

(next 2 will also repeat the previous 2 formations).

Answer 3

Probably the best way to work the question is to take 4 squares of paper and lay them out in different configurations. You are actually making a multiplication array. 1x4 vertically. 1x4 horizontally. 2x2 square. I think these are the only 3 arrangements.

Nope. How about 3 in a row horizontally with 1 on top to the left. 3 with 1 on bottom left. 3 with 1 on top right. 3 with 1 on bottom right.

Then do vertical groups of 3. I think that will make about 11 configurations.

Answer 4

Okay, Think about Tetris (am I getting old? Do you know what tetris is?) Each piece is comprised of 4 'blocks', but each piece can be rotated to 4 distinct positions so you have to be careful you're not counting it twice. There is the 4 long one, the L, the inverse of the L, the Z and it's inverse, and the square. That is 6 by my count.

Cheers!

Answer 5

one trick question