Concept 3 of 6
Symbol Equations: One Shape at a Time
Today's big idea
Solve the equation with only one shape first, then substitute that value into the other.
Every copy of a shape holds the same value, so one row unlocks the next.
How it works
👀 What's going on?
Two chocolate bars cost 8 rupees. You do not need anyone to tell you one bar costs 4. Symbol puzzles run on exactly that idea, only the bars are drawn as shapes, which makes them feel harder than they are.
💡 Here's the trick
The two rows above look equally hard, but they are not. The top row holds only stars, so it can be solved on its own: one star is 4. The bottom row holds a star and a triangle, and it only opens once you know the star.
🪄 How to do it
- 1.Scan the rows above and find the one with only a single kind of shape.
- 2.Solve that row on its own to get that shape's number.
- 3.Put that number into the other row and work out the second shape.
✍️ Try it
● + ● + ● = 9 and ● + ■ = 7. What is ■? Now the harder one: ◆ + ◆ = 14 and ◆ − ▲ = 2. What is ▲?
Three circles make 9, so one circle is 3, and 3 + ■ = 7 gives ■ = 4. In the second, two diamonds make 14, so a diamond is 7, and 7 − ▲ = 2 gives ▲ = 5.
⚠️ Watch out
You might be thinking the job is done the moment you crack the first shape. That is the trap the question is built around. Once you find ● = 3, read the question again. It asked for ■, and ■ is 4, not 3. Cracking the first shape is not the answer, it is the middle of the job.
🌟 Why this matters
Working out a price per item from a bundle is this same move: two bars for 8 rupees means 4 each. Later on the shapes become letters and the puzzle becomes algebra, so the habit of solving the easy row first pays for years.
Exam tip: Read the final line twice, because the trap option is nearly always the other shape.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“★ + ★ = 8 and ★ + △ = 10. Find △.”
- 1
Pick the easy equation
Equation 1 has only one shape (★). Solve it first. 💡
- 2
Solve for ★
★ + ★ = 8 means 2 × ★ = 8 → ★ = 4.
- 3
Substitute into Equation 2
4 + △ = 10 → △ = 6
- 4
Answer ✓
△ = 6
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Solve the equation with only ● first, then put its value into the other one.
SYMBOL EQUATION · ROUND 1 OF 3
● + ● = 10
● + ■ = 13
Quick check
✅ VERIFICATION
△ = 7 and ★ + △ = 11. What is ★ + ★?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Substitution Chain
Answer normally → look up the rename rule → final answer.