"This sudoku puzzle is really hard," said Sanguimenta. "But I'm not giving up!"
"You could try trial and error," suggested her sister Nonsequita. "How many different sudoku grids can there be, anyway?"
"Six sextillion, six hundred and seventy quintillion, nine hundred and three quadrillion, seven hundred and fifty-two trillion, twenty-one billion, seventy-two million, nine hundred and thirty-six thousand, nine hundred and sixty," said Sanguimenta instantly.
"Oh. How do you know that?"
"It's too complicated to explain."
"Then try something simpler. What about a smaller grid?"
"It would have to be four by four, instead of nine by nine…" said Sanguimenta, intrigued. She sketched furiously:
"I'll call it pseudoku," she said. "You have to put the numbers 1, 2, 3, 4 in each row, each column, and each 2x2 box."
"Can that be done?"
"Yes," said Sanguimenta. "But I wonder in how many different ways it can be done."
How many different pseudoku grids are there?
Scroll down for the answer
The answer
There are 288 different pseudoku grids in total.
There are 24 ways to permute the numbers 1, 2, 3, 4. So if we find all the combinations for a grid with a first row of 1234, we can multiply that number by 24 and find the total number of different grids. If the first row is 1234, the second row must be 3412, 3421, 4312, or 4321. For each of these second rows, trial and error shows that the grids can be completed in, respectively, 4, 2, 2, and 4 ways. So there are 12 grids with a top row of 1234, and 12x24=288.
The winner is Daphne Medley from Tavistock
