Place Value Riddles 5A worksheet with two riddles and multiple-choice answers for practicing place value skills.

Let's solve each riddle step by step using the clues provided.

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Riddle 1:

Clues:
1. I am larger than 3 million.
2. I am less than 3½ million (which is 3,500,000).
3. My largest digit is my ten thousands digit.
4. I am a multiple of 5.

Possible answers:
- 3,247,180
- 2,853,918
- 3,892,100
- 4,235,105
- 3,072,130
- 3,584,325
- 30,291,300
- 4,138,282

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#### Step 1: Eliminate numbers not between 3 million and 3.5 million.

So, we want:
> 3,000,000 < number < 3,500,000

Check each:

- 3,247,180 → ✔ (between 3M and 3.5M)
- 2,853,918 → ✘ (less than 3M)
- 3,892,100 → ✘ (greater than 3.5M)
- 4,235,105 → ✘ (too big)
- 3,072,130 → ✔
- 3,584,325 → ✘ (greater than 3.5M)
- 30,291,300 → ✘ (way too big)
- 4,138,282 → ✘ (too big)

So remaining candidates:
- 3,247,180
- 3,072,130

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#### Step 2: Check which is a multiple of 5.

A number is a multiple of 5 if it ends in 0 or 5.

- 3,247,180 → ends in 0 → ✔
- 3,072,130 → ends in 0 → ✔

Both are multiples of 5. So both pass this test.

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#### Step 3: "My largest digit is my ten thousands digit."

We need to identify the ten thousands digit — that’s the fifth digit from the right, or the digit in the 10,000s place.

Let’s break down both numbers:

a) 3,247,180

Digits:
3 (millions), 2 (hundred thousands), 4 (ten thousands), 7 (thousands), 1 (hundreds), 8 (tens), 0 (ones)

Wait! Let's write it properly with places:

| Millions | Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Ones |
|----------|-------------------|---------------|-----------|----------|------|------|
| 3 | 2 | 4 | 7 | 1 | 8 | 0 |

So:
- Ten thousands digit = 4
- Digits: 3, 2, 4, 7, 1, 8, 0 → largest digit is 8

Is 8 equal to the ten thousands digit? No → 8 ≠ 4 → ✘

So this one fails.

b) 3,072,130

Digits:

| Millions | Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Ones |
|----------|-------------------|---------------|-----------|----------|------|------|
| 3 | 0 | 7 | 2 | 1 | 3 | 0 |

Ten thousands digit = 7

Digits: 3, 0, 7, 2, 1, 3, 0 → largest digit is 7

Is 7 equal to the ten thousands digit? Yes → ✔

Also, ends in 0 → multiple of 5 → ✔

And it’s between 3M and 3.5M → ✔

✔ All conditions satisfied.

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✔ Answer to Riddle 1: 3,072,130

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Riddle 2:

Clues:
1. I am less than half a million → less than 500,000
2. My thousands digit is a multiple of 3
3. I am more than a quarter of a million → > 250,000
4. I am odd

Options:
- 347,283
- 1,206,311
- 4,286,135
- 814,277
- 233,117
- 416,532
- 379,513
- 2,130,767

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#### Step 1: Less than 500,000 → eliminate numbers ≥ 500,000

- 347,283 → ✔
- 1,206,311 → ✘ (over 1 million)
- 4,286,135 → ✘
- 814,277 → ✘ (over 800k)
- 233,117 → ✔
- 416,532 → ✔
- 379,513 → ✔
- 2,130,767 → ✘

Remaining:
347,283, 233,117, 416,532, 379,513

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#### Step 2: More than a quarter of a million → > 250,000

- 347,283 → ✔
- 233,117 → ✘ (less than 250k)
- 416,532 → ✔
- 379,513 → ✔

Now left: 347,283, 416,532, 379,513

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#### Step 3: I am odd → last digit must be odd

- 347,283 → ends in 3 → odd → ✔
- 416,532 → ends in 2 → even → ✘
- 379,513 → ends in 3 → odd → ✔

Now left: 347,283, 379,513

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#### Step 4: My thousands digit is a multiple of 3

Thousands digit is the fourth digit from the right.

Let’s find the thousands digit for each:

a) 347,283

Break down:
- 3 (hundred thousands)
- 4 (ten thousands)
- 7 (thousands) ← this is the thousands digit
- 2 (hundreds)
- 8 (tens)
- 3 (ones)

So thousands digit = 7

Is 7 a multiple of 3? 7 ÷ 3 = 2.33... → no → ✘

b) 379,513

Digits:
- 3 (hundred thousands)
- 7 (ten thousands)
- 9 (thousands) ← thousands digit
- 5 (hundreds)
- 1 (tens)
- 3 (ones)

Thousands digit = 9

Is 9 a multiple of 3? Yes → 9 ÷ 3 = 3 → ✔

All other conditions:
- Less than 500,000? → 379,513 < 500,000 → ✔
- Greater than 250,000? → yes → ✔
- Odd? → ends in 3 → ✔
- Thousands digit is multiple of 3? → 9 → ✔

✔ All conditions met.

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✔ Answer to Riddle 2: 379,513

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✔ Final Answers:

1) 3,072,130
2) 379,513

Let me know if you'd like an explanation in simpler terms!