Let's solve the problem step by step using the pattern shown in the image.
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Step 1: Identify the Pattern
Looking at the necklace:
The beads are arranged in a repeating pattern. Let's label them from left to right and identify their types:
1.
Spotty (checkerboard pattern)
2.
Stripy (diagonal lines)
3.
Plain (no pattern)
4.
Spotty
5.
Stripy
6.
Plain
7.
Spotty
8.
Stripy
9.
Plain
10.
Spotty
11.
Stripy
12.
Plain
So the pattern is:
Spotty → Stripy → Plain → Spotty → Stripy → Plain → ...
This is a
repeating cycle of 3 beads:
>
(Spotty, Stripy, Plain)
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Now let’s answer each question.
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1) How many beads are on the necklace now?
We count the beads in the picture:
There are
12 beads shown.
✔ Answer: 12
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2) What is the 5th bead – spotty, stripy or plain?
From above:
- 1st: Spotty
- 2nd: Stripy
- 3rd: Plain
- 4th: Spotty
-
5th: Stripy
✔ Answer: Stripy
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3) What is the 12th bead?
We already listed it:
- 12th:
Plain
✔ Answer: Plain
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4) How many spotty beads are there in total so far?
Spotty beads occur every 3rd position in the cycle: positions 1, 4, 7, 10.
So:
1st, 4th, 7th, 10th → that's
4 spotty beads
✔ Answer: 4
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5) Will the next bead be plain, stripy or spotty?
Current last bead is the 12th:
Plain
Next (13th) bead follows the pattern.
Pattern:
1. Spotty
2. Stripy
3. Plain
4. Spotty
...
So after
Plain, comes
Spotty
Thus, 13th bead =
Spotty
✔ Answer: Spotty
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6) Captain Salamander adds another 9 beads. How many beads are there now?
Original: 12 beads
Add: 9 beads
Total: 12 + 9 =
21 beads
✔ Answer: 21
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7) How many plain beads are there in the necklace now?
First, count plain beads in original 12 beads:
Plain beads appear at positions: 3, 6, 9, 12 → that’s
4 plain beads
Now, add 9 more beads: positions 13 to 21
We need to find how many of these new beads are
plain.
Recall the pattern repeats every 3 beads:
Positions modulo 3:
- If position ≡ 1 mod 3 → Spotty
- If position ≡ 2 mod 3 → Stripy
- If position ≡ 0 mod 3 → Plain
So for positions 13 to 21:
| Position | Mod 3 | Type |
|---------|-------|--------|
| 13 | 1 | Spotty |
| 14 | 2 | Stripy |
| 15 | 0 | Plain |
| 16 | 1 | Spotty |
| 17 | 2 | Stripy |
| 18 | 0 | Plain |
| 19 | 1 | Spotty |
| 20 | 2 | Stripy |
| 21 | 0 | Plain |
So plain beads added:
15, 18, 21 →
3 plain beads
Total plain beads now: 4 (original) + 3 (new) =
7
✔ Answer: 7
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8) Will the 20th bead be spotty, stripy or plain?
Position 20:
20 ÷ 3 = 6 remainder
2 → So 20 ≡ 2 mod 3 →
Stripy
✔ Answer: Stripy
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9) What would the last bead in the necklace be?
Last bead is the
21st bead
21 ÷ 3 = 7 remainder
0 → 21 ≡ 0 mod 3 →
Plain
✔ Answer: Plain
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✔ Final Answers:
1)
12
2)
Stripy
3)
Plain
4)
4
5)
Spotty
6)
21
7)
7
8)
Stripy
9)
Plain
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Let me know if you'd like this explained visually or with a table!
Parent Tip: Review the logic above to help your child master the concept of problem solving maths worksheet.
