Printable & Digital Logic Puzzles by Erins Classroom Creations | TPT - Free Printable

Let's solve the logic puzzle step by step using the clues provided.

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Problem: "How Old?"

Five cousins are playing at the park, and a park visitor asked each cousin their age. Use the clues below to discover the age of each cousin.

#### Clues:
1. Nathan is younger than Thomas.
2. Fiona is older than Nathan but younger than Thomas.
3. Charlotte is double the age of Ariana.

We are given a table with ages: 6, 9, 10, 12, 13 — one for each cousin.

The cousins are:
- Nathan
- Ariana
- Thomas
- Fiona
- Charlotte

We need to assign each person one unique age from the list.

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Step 1: List possible ages

Ages available: 6, 9, 10, 12, 13

We'll use logic to deduce who has which age.

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Step 2: Analyze Clue 1: *Nathan is younger than Thomas.*

So:
> Nathan < Thomas

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Step 3: Clue 2: *Fiona is older than Nathan but younger than Thomas.*

So:
> Nathan < Fiona < Thomas

This gives us an order:
Nathan < Fiona < Thomas

That means:
- Nathan is not the oldest.
- Thomas is not the youngest.
- Fiona is in between them.

So, among the three, Nathan is youngest, then Fiona, then Thomas.

Thus, we can eliminate some possibilities.

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Step 4: Clue 3: *Charlotte is double the age of Ariana.*

So:
> Charlotte = 2 × Ariana

Now look at the possible ages: 6, 9, 10, 12, 13

Which pairs satisfy "one is double the other"?

Check:

- 6 → 2×6 = 12 → Yes! (6 and 12)
- 9 → 2×9 = 18 → Not in list
- 10 → 2×10 = 20 → No
- 12 → 2×12 = 24 → No
- 13 → 2×13 = 26 → No

Only possibility: Ariana = 6, Charlotte = 12

OR

Wait: could Charlotte be 6 and Ariana be 3? But 3 is not in the list.

So only valid pair is:
> Ariana = 6, Charlotte = 12

Because 6 × 2 = 12.

So we now know:
- Ariana is 6
- Charlotte is 12

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Now, remaining ages: 9, 10, 13

Remaining people: Nathan, Thomas, Fiona

We also have:
> Nathan < Fiona < Thomas

So the three ages 9, 10, 13 must be assigned such that:
- Nathan gets the smallest (9)
- Fiona gets the middle (10)
- Thomas gets the largest (13)

Because only that satisfies: 9 < 10 < 13

So:
- Nathan = 9
- Fiona = 10
- Thomas = 13

Let’s check if this fits all clues.

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Check all clues:

1. Nathan < Thomas → 9 < 13 → ✔
2. Fiona > Nathan and Fiona < Thomas → 10 > 9 and 10 < 13 → ✔
3. Charlotte = 2 × Ariana → 12 = 2 × 6 → ✔

All clues satisfied!

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Final Assignments:

| Name | Age |
|-----------|-----|
| Nathan | 9 |
| Ariana | 6 |
| Thomas | 13 |
| Fiona | 10 |
| Charlotte | 12 |

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Fill in the answers:

Nathan's Age: 9
Ariana's Age: 6
Thomas's Age: 13
Fiona's Age: 10
Charlotte's Age: 12

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✔ Answer Completed!