Bonus Puzzle: Use the pattern to find the value of the '?'.

Let’s solve this step by step.

We have three triangles, each with numbers around them and one number on top. We need to find the pattern that connects the three side/bottom numbers to the top number.

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First triangle:
Top = 79
Left = 7
Right = 9
Bottom = 8

Try combining them:
Maybe (left × right) + bottom? → 7×9 = 63; 63+8 = 71 → too low.
Maybe (left + right) × something? 7+9=16; 16×5=80 — close but not 79.
Wait — what if we do: (left × 10) + (right × 1) + bottom?
→ 7×10 = 70; 9×1 = 9; 70+9+8 = 87 → no.

Another idea: Maybe it’s (left × right) + (bottom × something)?

Try: 7×9 = 63; 79 - 63 = 16 → and 16 is 2×8 → so maybe:
(left × right) + (2 × bottom) → 63 + 16 = 79 ✔ Works!

Check second triangle to verify:

Second triangle:
Top = 30
Left = 5
Right = 5
Bottom = 5

Apply same rule: (5×5) + (2×5) = 25 + 10 = 35 ✘ Not 30.

Hmm… doesn’t work.

Alternative idea: What if it’s (left + right + bottom) × something?

First triangle: 7+9+8 = 24 → 24 × ? = 79? No, 79 isn’t divisible by 24.

Wait — try this: Multiply left and right, then add bottom squared?

First: 7×9 = 63; 8² = 64 → 63+64=127 ✘ Too big.

What about: (left × bottom) + (right × something)?

Try first triangle: 7×8 = 56; 79-56=23 → 23 vs 9? Doesn’t fit.

Wait — let’s look at the third triangle for clues later. Let’s re-express all:

Triangle 1: Top=79, L=7, R=9, B=8
Triangle 2: Top=30, L=5, R=5, B=5
Triangle 3: Top=100, L=?, R=24, B=3 ← we need to find ?

Try a new approach: Maybe the top number is made from digits of the sides?

In Triangle 1: Left=7, Right=9 → “79” is exactly the top! But wait — bottom is 8. Why include bottom?

But in Triangle 2: Left=5, Right=5 → “55”, but top is 30 → doesn’t match.

Unless... maybe it’s (left × 10) + right only when bottom is ignored? But then why is bottom there?

Wait — look again at Triangle 1: 7, 9, 8 → top is 79. That’s just left and right put together as digits.

Triangle 2: 5,5,5 → if you put left and right together: 55, but top is 30 → doesn’t match.

BUT — 5×5 + 5 = 30? 25+5=30 ✔ Oh! Wait — that works for Triangle 2.

So for Triangle 2: (left × right) + bottom = 5×5 + 5 = 30 ✔

Now check Triangle 1: (7×9) + 8 = 63 + 8 = 71 ✘ But top is 79.

Not matching.

Wait — what if it’s (left × 10) + right + bottom?

Triangle 1: 7×10=70; +9=79; +8=87 ✘

No.

Another idea: Maybe it’s (left + bottom) × right?

Triangle 1: (7+8)=15; 15×9=135 ✘

Too big.

Wait — let’s try this:

What if the top number is: (left × right) + (bottom × k), and we solve for k using Triangle 2?

Triangle 2: 5×5 + 5k = 30 → 25 + 5k = 30 → 5k=5 → k=1

Then for Triangle 1: 7×9 + 8×1 = 63+8=71 ≠79 ✘

Doesn’t work.

Wait — what if it’s (left × bottom) + (right × something)?

Try Triangle 2: 5×5 + 5×x = 30 → 25 + 5x = 30 → x=1 → so (L×B) + (R×1)

Test on Triangle 1: (7×8) + (9×1) = 56+9=65 ✘ Not 79.

Still no.

Let me think differently.

Look at Triangle 3: Top=100, Right=24, Bottom=3, Left=?

If I assume the formula is symmetric or based on multiplication...

What if top = (left + right) × bottom?

Triangle 2: (5+5)×5 = 10×5=50 ✘ Not 30.

Triangle 1: (7+9)×8=16×8=128 ✘

No.

Wait — here's an idea:

What if the top number is formed by multiplying two of the numbers and adding the third, but which ones?

Try for Triangle 1: Suppose top = (left × bottom) + right → 7×8 +9=56+9=65 ✘

Or (right × bottom) + left → 9×8 +7=72+7=79 ✔ YES!

Check Triangle 2: (right × bottom) + left = 5×5 +5=25+5=30 ✔ YES!

Perfect! So the pattern is:

> Top = (Right × Bottom) + Left

Verify with Triangle 1: Right=9, Bottom=8, Left=7 → 9×8 +7 = 72+7=79 ✔
Triangle 2: Right=5, Bottom=5, Left=5 → 5×5 +5=25+5=30 ✔

Great! Now apply to Triangle 3:

Top = 100
Right = 24
Bottom = 3
Left = ?

Formula: Top = (Right × Bottom) + Left
→ 100 = (24 × 3) + ?
→ 100 = 72 + ?
→ ? = 100 - 72 = 28

✔ Checks out.

Final Answer:
28