House of Hundreds - II

Given number: 832

We break 832 into hundreds, tens, and ones:
$$832 = 800 + 30 + 2$$

- Hundreds: 8 big tiles (each representing 100)
- Tens: 3 medium tiles (each representing 10)
- Ones: 2 small tiles (each representing 1)

Draw 8 hundred-tiles, 3 ten-tiles, and 2 one-tiles in your notebook.

Given number: 947

We break 947 into hundreds, tens, and ones:
$$947 = 900 + 40 + 7$$

- Hundreds: 9 big tiles
- Tens: 4 medium tiles
- Ones: 7 small tiles

Draw 9 hundred-tiles, 4 ten-tiles, and 7 one-tiles in your notebook.

Given number: 726

We break 726 into hundreds, tens, and ones:
$$726 = 700 + 20 + 6$$

- Hundreds: 7 big tiles
- Tens: 2 medium tiles
- Ones: 6 small tiles

Draw 7 hundred-tiles, 2 ten-tiles, and 6 one-tiles in your notebook.

Given number: 504

We break 504 into hundreds, tens, and ones:
$$504 = 500 + 0 + 4$$

- Hundreds: 5 big tiles
- Tens: 0 medium tiles (none)
- Ones: 4 small tiles

Draw 5 hundred-tiles and 4 one-tiles in your notebook. There are no ten-tiles.

Given number: 620

We break 620 into hundreds, tens, and ones:
$$620 = 600 + 20 + 0$$

- Hundreds: 6 big tiles
- Tens: 2 medium tiles
- Ones: 0 small tiles (none)

Draw 6 hundred-tiles and 2 ten-tiles in your notebook. There are no one-tiles.

Given number: 700

We break 700 into hundreds, tens, and ones:
$$700 = 700 + 0 + 0$$

- Hundreds: 7 big tiles
- Tens: 0 medium tiles (none)
- Ones: 0 small tiles (none)

Draw 7 hundred-tiles in your notebook. There are no ten-tiles or one-tiles.

We place each number on the number line between 500 and 700.

- $530$ lies between 500 and 600, closer to 500. It is 3 tens after 500.
- $540$ lies between 500 and 600. It is 4 tens after 500.
- $590$ lies between 500 and 600, very close to 600. It is 9 tens after 500.
- $628$ lies between 600 and 700, closer to 600. It is 2 tens and 8 ones after 600.
- $696$ lies between 600 and 700, very close to 700. It is 9 tens and 6 ones after 600.

On the number line, mark these points in order: $530, 540, 590, 628, 696$.

We place each number on the number line between 700 and 900.

- $703$ lies just after 700 (3 ones after 700).
- $721$ lies between 700 and 800, closer to 700 (2 tens and 1 one after 700).
- $759$ lies between 700 and 800, closer to 800 (5 tens and 9 ones after 700).
- $810$ lies between 800 and 900, closer to 800 (1 ten after 800).
- $855$ lies between 800 and 900, in the middle (5 tens and 5 ones after 800).
- $887$ lies between 800 and 900, closer to 900 (8 tens and 7 ones after 800).

On the number line, mark these points in order: $703, 721, 759, 810, 855, 887$.

We find the neighbouring hundreds (multiples of 100), neighbouring fifties (multiples of 50), and neighbouring tens (multiples of 10) for each number.

183:
- Neighbouring Hundreds: $100$ and $200$ (since $100 < 183 < 200$)
- Neighbouring Fifties: $150$ and $200$ (since $150 < 183 < 200$)
- Neighbouring Tens: $180$ and $190$ (since $180 < 183 < 190$)

345:
- Neighbouring Hundreds: $300$ and $400$ (since $300 < 345 < 400$)
- Neighbouring Fifties: $300$ and $350$ (since $300 < 345 < 350$)
- Neighbouring Tens: $340$ and $350$ (since $340 < 345 < 350$)

693:
- Neighbouring Hundreds: $600$ and $700$ (since $600 < 693 < 700$)
- Neighbouring Fifties: $650$ and $700$ (since $650 < 693 < 700$)
- Neighbouring Tens: $690$ and $700$ (since $690 < 693 < 700$)

734:
- Neighbouring Hundreds: $700$ and $800$ (since $700 < 734 < 800$)
- Neighbouring Fifties: $700$ and $750$ (since $700 < 734 < 750$)
- Neighbouring Tens: $730$ and $740$ (since $730 < 734 < 740$)

899:
- Neighbouring Hundreds: $800$ and $900$ (since $800 < 899 < 900$)
- Neighbouring Fifties: $850$ and $900$ (since $850 < 899 < 900$)
- Neighbouring Tens: $890$ and $900$ (since $890 < 899 < 900$)

Completed Table:

| Number | Neighbouring Hundreds | Neighbouring Fifties | Neighbouring Tens |
|---|---|---|---|
| 468 | 400 and 500 | 450 and 500 | 460 and 470 |
| 183 | 100 and 200 | 150 and 200 | 180 and 190 |
| 345 | 300 and 400 | 300 and 350 | 340 and 350 |
| 693 | 600 and 700 | 650 and 700 | 690 and 700 |
| 734 | 700 and 800 | 700 and 750 | 730 and 740 |
| 899 | 800 and 900 | 850 and 900 | 890 and 900 |

Crane 1 — To reach the worm (going left/backward):

Given: $667 - ? = 650$

$$667 - 650 = 17$$

So the crane takes 17 steps (each step of length 1), or it can take 1 step of 10 and 1 step of 7, or 1 step of 17.

Answer: $667 - 17 = 650$. Number of steps: 17 (or 2 jumps: first 10, then 7).

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Crane 1 — To reach the fish (going right/forward):

Given: $667 + ? = 700$

$$700 - 667 = 33$$

So the crane takes 33 steps, or it can take 1 step of 30 and 1 step of 3, or 1 step of 33.

Answer: $667 + 33 = 700$. Number of steps: 33 (or 2 jumps: first 30, then 3).

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Crane 2 — To reach the worm (going left/backward):

The crane is standing at some number and needs to reach 750. Based on the number line context (the second crane appears to be near 780):

Given: $780 - ? = 750$

$$780 - 750 = 30$$

Answer: $780 - 30 = 750$. Number of steps: 30.

*(Note: The exact starting position of Crane 2 depends on the figure. If the crane stands at 780, then 30 steps back reaches 750.)*

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Crane 2 — To reach the fish (going right/forward):

Given: $780 + ? = 800$

$$800 - 780 = 20$$

Answer: $780 + 20 = 800$. Number of steps: 20.

Let us apply each clue to the grid:

Clue 1: 597
- Strike out: 597 ✓

Clue 2: A number with digit 4
- Numbers in grid containing digit 4: 574, 614
- Strike out: 574, 614 ✓

Clue 3: Numbers between 595 and 605
- Numbers strictly between 595 and 605: 596, 597, 598, 599, 600, 601, 602, 603, 604
- Numbers in grid: 599, 597 (already struck), 600, 602
- Strike out: 599, 600, 602 ✓ (597 already done)

Clue 4: A number with 1 as the tens digit
- Tens digit = 1 means numbers like _1_: 610–619
- Numbers in grid: 616, 614 (already struck)
- Strike out: 616 ✓

Clue 5: Two more than 610
- $610 + 2 = 612$
- 612 is not in the given grid, so no number to strike out from the grid for this clue.

Clue 6: 5 less than 625
- $625 - 5 = 620$
- 620 is not in the given grid, so no number to strike out from the grid for this clue.

Summary of numbers struck out from the grid:
- Clue 1: 597
- Clue 2: 574, 614
- Clue 3: 599, 600, 602
- Clue 4: 616

Total numbers struck out: 7 (597, 574, 614, 599, 600, 602, 616)

Note: The exact centre numbers depend on the figures which are not fully visible. The method is shown below using examples.

Example for 456:
$$456 = 400 + 50 + 6$$
$$456 = 400 + 56$$
$$456 = 450 + 6$$
$$456 = 460 - 4$$
$$456 = 500 - 44$$

Example for 321:
$$321 = 300 + 20 + 1$$
$$321 = 300 + 21$$
$$321 = 320 + 1$$
$$321 = 330 - 9$$
$$321 = 400 - 79$$

Write as many number sentences as you can for the number given in the centre of your figure.

Note: The exact conditions depend on the figures. The general method is:

- Read the condition carefully (e.g., 'greater than 500 and less than 600').
- Think of numbers that satisfy all the given conditions.
- Write those numbers in the blank spaces.

Example: If the condition is: greater than 400, less than 500, has 3 in the tens place:
- Possible answers: 430, 431, 432, 433, 434, 435, 436, 437, 438, 439

Fill in numbers that satisfy all the conditions shown in your figure.