Math worksheet titled "Place Value Riddles 4B" with two riddle problems and multiple-choice answers, featuring a cartoon salamander and the Math-Salamanders.com logo.

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

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Riddle 1:

Clues:
1. I am not divisible by 2 → The number is odd.
2. I am less than seven hundred thousand → Number < 700,000.
3. My thousands digit is half of my tens digit.
4. My hundred thousands digit is greater than 4.

Options:
- 482,549
- 389,326
- 528,345
- 626,231
- 701,429
- 528,347
- 613,266
- 591,427

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#### Step 1: Eliminate numbers divisible by 2 (i.e., even numbers)
Even numbers end in 0, 2, 4, 6, or 8.

Eliminate:
- 389,326 → ends in 6 → even ✘
- 613,266 → ends in 6 → even ✘
- 701,429 → odd ✔
- 482,549 → odd ✔
- 528,345 → odd ✔
- 626,231 → odd ✔
- 528,347 → odd ✔
- 591,427 → odd ✔

Remaining:
482,549; 528,345; 626,231; 701,429; 528,347; 591,427

Wait — actually, let’s list only the odd ones:

- 482,549 → odd ✔
- 528,345 → odd ✔
- 626,231 → odd ✔
- 701,429 → odd ✔
- 528,347 → odd ✔
- 591,427 → odd ✔

So we eliminate:
- 389,326 ✘
- 613,266 ✘

Now left with:
482,549; 528,345; 626,231; 701,429; 528,347; 591,427

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#### Step 2: Less than 700,000

So eliminate any number ≥ 700,000

- 701,429 → 701,429 > 700,000 ✘

Now remaining:
- 482,549
- 528,345
- 626,231
- 528,347
- 591,427

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#### Step 3: Hundred thousands digit > 4

Look at the hundred thousands digit (the first digit):

- 482,549 → 4 → not > 4 ✘
- 528,345 → 5 → > 4 ✔
- 626,231 → 6 → > 4 ✔
- 528,347 → 5 → > 4 ✔
- 591,427 → 5 → > 4 ✔

So eliminate: 482,549 ✘

Now remaining:
- 528,345
- 626,231
- 528,347
- 591,427

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#### Step 4: Thousands digit is half of tens digit

Let’s break down each number:

##### a) 528,345
- Digits: 5 (hundred thousands), 2 (ten thousands), 8 (thousands), 3 (hundreds), 4 (tens), 5 (ones)
- Thousands digit = 8
- Tens digit = 4
- Is 8 = half of 4? No → 8 ≠ 2 → ✘

But wait: “Thousands digit is half of tens digit” → So:
Thousands digit = (1/2) × tens digit

So: 8 = (1/2) × 4 → 8 = 2 → false ✘

##### b) 626,231
- Digits: 6, 2, 6, 2, 3, 1
- Thousands digit = 6
- Tens digit = 3
- Is 6 = (1/2) × 3? → 6 = 1.5? ✘

No.

##### c) 528,347
- Digits: 5, 2, 8, 3, 4, 7
- Thousands digit = 8
- Tens digit = 4
- Is 8 = (1/2) × 4? → 8 = 2? ✘

No.

##### d) 591,427
- Digits: 5, 9, 1, 4, 2, 7
- Thousands digit = 1
- Tens digit = 2
- Is 1 = (1/2) × 2? → 1 = 1 → ✔ YES!

So this satisfies all conditions?

Let’s verify all clues for 591,427:

1. Not divisible by 2 → ends in 7 → odd → ✔
2. Less than 700,000 → 591,427 < 700,000 → ✔
3. Thousands digit = 1, tens digit = 2 → 1 = half of 2 → ✔
4. Hundred thousands digit = 5 > 4 → ✔

✔ All clues satisfied.

Wait — but earlier we had 528,345 and others — did we miss one?

Let’s double-check if any other number could work.

Wait — what about 528,345?

We said:
- Thousands digit = 8
- Tens digit = 4
- Is 8 = half of 4? → no → 8 = 2? → no.

But what if it's the other way? "My thousands digit is half of my tens digit"

So: thousands = (1/2) × tens

So tens must be even, and thousands = half of that.

So possible values:
- If tens = 2 → thousands = 1
- tens = 4 → thousands = 2
- tens = 6 → thousands = 3
- tens = 8 → thousands = 4

So thousands digit must be ≤ 4, and tens digit = 2×thousands.

So check each remaining number:

- 528,345 → thousands=8, tens=4 → 8 = ½ × 4? → no
- 626,231 → thousands=6, tens=3 → 6 = ½ × 3? → no
- 528,347 → thousands=8, tens=4 → same → no
- 591,427 → thousands=1, tens=2 → 1 = ½ × 2 → yes ✔

Only one satisfies: 591,427

✔ So Answer to Riddle 1: 591,427

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Riddle 2:

Clues:
1. I am a multiple of 4.
2. My hundreds digit is two less than my hundred thousands digit.
3. If you multiply me by 10, then my value is less than 3 million.
4. If you round me to the nearest 10, then I round up.

Options:
- 526,312
- 227,056
- 59,368
- 107,340
- 163,388
- 216,038
- 192,044
- 316,128

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#### Step 1: Multiple of 4

A number is divisible by 4 if its last two digits form a number divisible by 4.

Check each:

- 526,312 → last two: 12 → 12 ÷ 4 = 3 → ✔
- 227,056 → 56 ÷ 4 = 14 → ✔
- 59,368 → 68 ÷ 4 = 17 → ✔
- 107,340 → 40 ÷ 4 = 10 → ✔
- 163,388 → 88 ÷ 4 = 22 → ✔
- 216,038 → 38 ÷ 4 = 9.5 → ✘
- 192,044 → 44 ÷ 4 = 11 → ✔
- 316,128 → 28 ÷ 4 = 7 → ✔

So eliminate: 216,038 ✘

Remaining:
- 526,312
- 227,056
- 59,368
- 107,340
- 163,388
- 192,044
- 316,128

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#### Step 2: Multiply by 10 → value < 3 million

So: number × 10 < 3,000,000 → number < 300,000

So eliminate any number ≥ 300,000

- 526,312 → > 300,000 ✘
- 316,128 → > 300,000 ✘

Remaining:
- 227,056
- 59,368
- 107,340
- 163,388
- 192,044

All are < 300,000 → OK ✔

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#### Step 3: Hundreds digit is two less than hundred thousands digit

Let’s define:

- Hundred thousands digit = digit in the 100,000s place
- Hundreds digit = digit in the 100s place

So: hundreds digit = hundred thousands digit - 2

Check each:

##### a) 227,056
- Hundred thousands digit = 2
- Hundreds digit = 0
- Is 0 = 2 - 2? → 0 = 0 → ✔

Yes!

##### b) 59,368
- This is only 5-digit number → hundred thousands digit = 0? But it's written as 59,368 → so it's 059,368? But usually we don’t write leading zero.

But the number is 59,368 → so:
- Hundred thousands digit = 0 (since it's less than 100,000)
- Hundreds digit = 3
- Is 3 = 0 - 2? → 3 = -2? ✘

No.

Also, hundred thousands digit is 0 → so hundreds digit should be 0 - 2 = -2 → impossible.

So ✘

##### c) 107,340
- Hundred thousands digit = 1
- Hundreds digit = 3
- Is 3 = 1 - 2? → 3 = -1? ✘

No.

##### d) 163,388
- Hundred thousands digit = 1
- Hundreds digit = 3
- 3 = 1 - 2? → 3 = -1? ✘

No.

##### e) 192,044
- Hundred thousands digit = 1
- Hundreds digit = 0
- Is 0 = 1 - 2? → 0 = -1? ✘

No.

Only 227,056 satisfies this clue.

✔ So far, only 227,056 passes all three so far.

Let’s check the last clue.

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#### Step 4: If you round me to the nearest 10, then I round up.

This means: the ones digit is 5 or more → because rounding up happens when the ones digit ≥ 5.

So check ones digit of 227,056 → last digit = 6 → ≥ 5 → rounds up → ✔

Perfect.

Let’s confirm all clues for 227,056:

1. Multiple of 4 → last two digits: 56 → 56 ÷ 4 = 14 → ✔
2. Hundreds digit = 0, hundred thousands digit = 2 → 0 = 2 - 2 → ✔
3. Multiply by 10: 227,056 × 10 = 2,270,560 < 3,000,000 → ✔
4. Rounds up to nearest 10 → ends in 6 → rounds up → ✔

✔ All clues satisfied.

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✔ Final Answers:

1) 591,427
2) 227,056

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✔ Boxed Answers:

1) $\boxed{591,427}$
2) $\boxed{227,056}$