Colorado Smith and Brunnhilde heaved their weary bodies on to the top terrace of the lost city of Muchu Poochu and lay panting on the flagstones. The city was named for an ancient dog god—still worshipped there, according to the traditional bloody rituals of the Inctecayas—and its sacred temples were guarded by hundreds of fierce wolfhounds. The intrepid pair could hear them prowling in the darkness.
"That was a piece of cake," said Smith. "Now, remind me how we secure the riches of the Treasury of Poochihuahua."
"We have to answer the riddle of Muchu Poochu," said Brunnhilde. "You wrote it down in your father's old notebook. Don't tell me you've lost it again—"
"I have it tucked safely in my sock. We need the secret number of the Inctecayas."
"Which is?"
"It's implicit in the form of the plaza of the reborn dog—which is composed of 12 square slabs arranged in a 3x4 rectangle. The secret number is the total number of different ways, including reflections and rotations, to choose four of those slabs that form a connected region. Slabs are connected if they share a common edge; they can't just touch at their corners."
"And what is that number, then?" said Brunnhilde, paling at the sound of baying.
"I haven't done the calculations yet," admitted Smith. "But I'm sure we can work it out, since there's no pressure—"
What is the secret number?
Competition
Prospect invites you to solve the puzzle and send us the solution. Correct answers will be entered into a draw. The winner will receive Pythagoras' Revenge: A Mathematical Mystery by Arturo Sangalli (Princeton University Press, £14.95).
Send your solution to answer@prospect-magazine.co.uk by 10th July.
The winner will be announced in our August issue. Last month's winner wasAlastair Summers, Stamford
Last month's answer
Take the chains of three and four links, break each link and use these to join the seven other pieces. The total cost is £42.
