This puzzle consists completely of binary numbers, so all the characters needed

Question

This puzzle consists completely of binary numbers, so all the characters needed to fill in the squares will be 0s or 1s. The crossword is a 4x4 square grid, so all numbers will be written in binary, with 4 digits; e.g., 1 will be 0001, 2 will be 0010, and 4, 0100. The NOT operation changes all 0s to 1's and all 1s to 0s; e.g., NOT(0110) is 1001 and NOT(1010) is 0101.

Rows (Across):

1. "2 Down" x 2

2. A triangular number *

3. The cube of ("4 Down" - 2)

4. "3 Across" + "3 Down"

Columns (Down):

1. NOT "2 Across"

2. NOT "1 Across"

3. "2 Across" x 2

4. "4 Across" - "1 Across"

* HINT: A triangular number is the number of dots in an equilateral triangle uniformly filled with dots. For example, three dots can be arranged in a triangle; thus three is a triangle number.

Rows (Across):

1. "2 Down" x 2

2. A triangular number *

3. The cube of ("4 Down" - 2)

4. "3 Across" + "3 Down"

Columns (Down):

1. NOT "2 Across"

2. NOT "1 Across"

3. "2 Across" x 2

4. "4 Across" - "1 Across"

* HINT: A triangular number is the number of dots in an equilateral triangle uniformly filled with dots. For example, three dots can be arranged in a triangle; thus three is a triangle number.

Explanation / Answer

Ans: The trick to sloving this puzzle is the clue for 2 Across. Triangular number are numbers for which the number of objects can be arranged to form regular triangles. Those numbers include 1,3,6,10,15,21,28,... since we know that our binary number must fit within 4bits, we are limited to the numbers 1,3,6,10, and 15, The clue for 3 down states that 2 Across must be less than 8 (otherwise ''2 Across x 2'' would be too large to fit in 4bits), so we are left with 2 Across being either 1,3, or 6 .

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