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Friday, January 25, 2008

A Binary Crossnumber Puzzle

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"


Steve said...
Please can you tell us the answer to this puzzle.

Erik said...


There are two clues which will lead to the solution.

A) 2 Across is a triangular number. The triangular numbers that will fit in 4 bits are 1, 3, 6, 10, and 15. However, since 3 Down is twice the value of 2 Across the values 10 and 15 can be eliminated.

B) 3 Across is the cube of (4 Down - 2). There are only two cube values that will fit in 4 bits, 1 and 8. If you start with the value 8, then the value of 4 Down has to be 4. However, this causes a problem because 2 Across will be an odd value, and 3 Down is twice the value of 2 Across requiring a '1' bit in the third position of 3 Across.

That should be enough to get you to the solution fairly quickly.

Nagendra Kumar said...