Brain Out Level 66

Overview

The prompt "Find out the rule and write down the answer!" shows a table of seven rows. Each row has five symbols — either an empty circle O or a filled triangle △ — followed by an equals sign and a number. The first six rows give you the mapping: OOOOO = 0, OOOO△ = 1, OOO△O = 2, OOO△△ = 3, OO△O△ = 5, OO△△O = 6, and the last row O△OO△ = ? asks for the answer.

• Difficulty: Hard
• Estimated moves: 2

Step-by-Step Solution

1. Treat the empty circle O as the digit 0 and the filled triangle △ as the digit 1.
2. Read each row from left to right as a five-bit binary number. The first row OOOOO is 00000 which equals 0, matching the given value.
3. The second row OOOO△ is 00001 which equals 1, matching. The third OOO△O is 00010 which equals 2. The fourth OOO△△ is 00011 which equals 3. The fifth OO△O△ is 00101 which equals 5. The sixth OO△△O is 00110 which equals 6. All given rows confirm the binary interpretation.
4. The last row is O△OO△. Convert it to binary: 0 1 0 0 1.
5. Compute the value: 016 + 18 + 04 + 02 + 1*1 = 9.
6. Type 9 into the input field and press OK. The congratulations popup says "You've got your brain in gear today!"

Each row has five symbols: either an empty circle O or a filled triangle. The given outputs are 0, 1, 2, 3, 5, and 6. Treat O as 0 and triangle as 1.

Read each row left to right as a five-bit binary number. The given rows check out: 00000=0, 00001=1, 00010=2, 00011=3, 00101=5, 00110=6. The last row O triangle O O triangle is 01001 in binary, which equals 9. Type 9 and press OK.

Type 9 into the input field. The row O triangle O O triangle reads 01001 in binary, which is 9. If you type any other number, the level rejects it. The binary rule is consistent across all given rows.

Strategy & Reasoning

The table is a binary cipher. The circles and triangles are just stand-ins for 0 and 1, and the numbers on the right are the decimal values of those five-bit binary strings. Once you see that △ is 1 and O is 0, every given row checks out perfectly. The last row O△OO△ decodes to 01001, which is binary for 9. There is no trick beyond reading the symbols as binary digits.

Tips & Common Mistakes

• Do not try to count triangles in each row. The first row has zero triangles and equals 0, but the fifth row has two triangles and equals 5 — so triangle count alone is not the rule.
• Do not read the binary right-to-left. The leftmost symbol is the highest bit (16s place).
• Do not answer 5 or 3. Those are values from earlier rows, not the last one.