Parmjit has 8 base ten blocks. She has at least one of each type of block. The value of her blocks is between 400 and 600. What blocks could she have? Find the possible answers using an organized list.

1) There are 3 Hundreds:

among the 7 remaining blocks, at least 5 must be tens and the other 2 block can either be tens or one ---> 2^2 = 4 possibilities!!
2) There are 4 Hundreds:
the 6 remaining blocks can either be tens or ones ---> 2^6 = 64 possibilities!!
3) There are 5 Hundreds:
the 5 remaining blocks can either be tens or ones---> 2^5 = 32 possibilities!!
You have 4 + 64 + 32 = 100 possibilities!!!

To find the possible blocks Parmjit could have, let's consider the value of each type of block and create an organized list:

1. Thousands block (value 1000):
It is not possible for Parmjit to have any thousands blocks, as the value of her blocks is between 400 and 600.

2. Hundreds block (value 100):
Parmjit cannot have more than 5 hundreds blocks since the value of her blocks is between 400 and 600 (and 6 hundreds blocks would already exceed 600). Let's analyze the possibilities:

a) Parmjit has 5 hundreds blocks:
The total value of the hundreds blocks would be 5 * 100 = 500.
Parmjit would have 8 - 5 = 3 blocks remaining.

- Parmjit could have 3 tens blocks (value 10).
The total value of the tens blocks would be 3 * 10 = 30.
To reach a total value of 400, Parmjit would still need 400 - 500 - 30 = -130, which is not possible.

- Parmjit could have 2 tens blocks (value 10) and 1 ones block (value 1).
The total value of the tens blocks would be 2 * 10 = 20.
The total value of the ones block would be 1 * 1 = 1.
To reach a total value of 400, Parmjit would still need 400 - 500 - 20 - 1 = -121, which is not possible.

b) Parmjit has 4 hundreds blocks:
The total value of the hundreds blocks would be 4 * 100 = 400.
Parmjit would have 8 - 4 = 4 blocks remaining.

- Parmjit could have 4 tens blocks (value 10).
The total value of the tens blocks would be 4 * 10 = 40.
To reach a total value of 400, Parmjit would not need any ones blocks.
Therefore, Parmjit could have 4 hundreds blocks, 4 tens blocks, and no ones blocks.

Based on the analysis, Parmjit could have the following blocks:
- 4 hundreds blocks (value 100 each)
- 4 tens blocks (value 10 each)
- 0 ones blocks (value 1 each)

Therefore, the possible blocks Parmjit could have are: 4 hundreds blocks, 4 tens blocks, and 0 ones blocks.

To find the possible blocks Parmjit could have, we need to consider the value range of 400 to 600. Each base ten block represents a place value: ones, tens, hundreds, and so on. Let's start by listing the possible combinations of blocks that fall within the given value range.

We know that Parmjit has at least one of each type of block, so there are three possible cases:

Case 1: Parmjit has one hundred block.

In this case, the value of the hundred block alone is 100. To reach a total value between 400 and 600, we need to consider the tens and ones blocks. The maximum value for each of the tens and ones blocks is 9, as Parmjit has at least one of each type of block. Let's list the possible combinations:

1 hundred block + 0 tens blocks + 0 ones blocks = 100
1 hundred block + 0 tens blocks + 1 ones block = 101
1 hundred block + 0 tens blocks + 2 ones blocks = 102
...
1 hundred block + 9 tens blocks + 0 ones blocks = 190
1 hundred block + 9 tens blocks + 1 ones block = 191
1 hundred block + 9 tens blocks + 2 ones blocks = 192
...
1 hundred block + 9 tens blocks + 9 ones blocks = 199

Case 2: Parmjit has one ten block.

In this case, the value of the ten block alone is 10. Following a similar pattern, let's list the possible combinations:

0 hundred blocks + 1 ten block + 0 ones blocks = 10
0 hundred blocks + 1 ten block + 1 ones block = 11
0 hundred blocks + 1 ten block + 2 ones blocks = 12
...
9 hundred blocks + 1 ten block + 0 ones blocks = 910
9 hundred blocks + 1 ten block + 1 ones block = 911
9 hundred blocks + 1 ten block + 2 ones blocks = 912
...
9 hundred blocks + 1 ten block + 9 ones blocks = 919

Case 3: Parmjit has no hundred or ten blocks, only ones blocks.

In this case, the value of the ones block alone is 1. Again, let's list the possible combinations:

0 hundred blocks + 0 ten blocks + 4 ones blocks = 4
0 hundred blocks + 0 ten blocks + 5 ones blocks = 5
0 hundred blocks + 0 ten blocks + 6 ones blocks = 6
...
9 hundred blocks + 0 ten blocks + 4 ones blocks = 904
9 hundred blocks + 0 ten blocks + 5 ones blocks = 905
9 hundred blocks + 0 ten blocks + 6 ones blocks = 906
...
9 hundred blocks + 0 ten blocks + 9 ones blocks = 909

By organizing the above lists, we can see all the possible combinations of blocks for Parmjit:

100, 101, 102, ..., 199
10, 11, 12, ..., 19
4, 5, 6, ..., 9
910, 911, 912, ..., 919
14, 15, 16, ..., 19
904, 905, 906, ..., 909

These are the possible answers, representing the different combinations of blocks Parmjit could have.

where are 307