*Solve simple logical thinking puzzles and gain a deeper understanding of binary and how it is based on powers of two.** *

Puzzles are a good way of developing computational thinking. Bakuro, or Revelations puzzles, are very simple logical thinking puzzles, that are a fun way to learn about the binary representation of numbers.

Bakuro are binary versions of the popular Kakuro puzzle. The empty cells of the grid must be filled with the numbers 1, 2, 4 and 8 (i.e., only powers of 2). As with Kakuro, the numbers in each block in a column or row must add up to the number given in the clue above or to the left, respectively. No number can be used twice within any sum. The clues are given in both binary and decimal. The answers must also be written in both binary and decimal.

**Learn about:**

- binary representation of numbers
- data representation
- logical thinking
- computational thinking

**Example:**

Here is a small example, together with its solution. Download large puzzles to try at the bottom of the page.

**Logical Thinking**

We can deduce the answer by noticing that the top row adds up to 3. The only way this can be done with the numbers 1,2,4 and 8 is with 1 + 2. Now the leftmost column must add up to 9, so it must be 1 + 8. The top left cell must hold a number from both those sums, which means it must be 1 (0001 in binary) as that is the only number common to the two sums.

Now if the top left cell hold 1, then the top right cell must hold 2 (0010 in binary) to make the row add up to 3. Similarly, the bottom right column must be 8 (1000) to make the leftmost column add to 9. That leaves the bottom right cell. It must hold 4 as the bottom row has to add up to 12 (8 + 4). That also makes the rightmost column add to 6 as required.

**Computational Thinking Hint**

Binary numbers are just a way of making up numbers by adding powers of 2 (1, 2, 4, 8, …) together, just like decimal numbers involve adding powers of 10 (1, 10, 100, 1000) together.

Have you noticed any patterns in the numbers? The answers that go in the grid only have a single 1 in their binary representation. The binary of the clue actually tells you which numbers you are looking for. 12 is 1100 in binary which says that 12 is made up of one 8 and one 4 with no 2s and no units, added together. The row must therefore hold an 8 and a 4. Similarly, 9 is 1001 in binary (one 8, no 4s, one 2 and one unit added together) so its column must hold an 8 and a 1.

Watch out for our computational thinking puzzle book, coming in the Spring of 2016.

**Resources: Bakuro puzzles**

Here are some computer science linked Bakuro puzzle sheets that you can download:

- Puzzle Sheet: Bakuro Puzzle Sheet 1 [PDF]
- Solution Sheet: Solution to Bakuro 1 [PDF]
- Puzzle Sheet: Bakuro Puzzle Sheet 2 [PDF]
- Solution Sheet: Solution to Bakuro 2 [PDF]
- Slides: Bakuro Binary Logical Thinking Puzzles [PPT]
- Slides: Bakuro Binary Logical Thinking Puzzles [PDF]

**Resources: Blank Puzzle Grids**

It can also be a good follow-up activity to create your own Bakuro puzzles, either drawing the grid yourself, or using blank puzzle grids such as those below:

- Blank Puzzle Grids: Blank 3×3, 7×7, 8×8 and 10×10 Grids [PDF]