Today is the one year anniversary of the best-worst day of your life. The best part was discovering a subterranean city on Mars: the first evidence of intelligent alien life ever found. The worst part? No one got to explore it, because that was when you lost contact with Earth. You and the other 99 scientists have spent the rest of the year engineering your survival, but you’re almost out of water and solutions.
Everyone else is at the ice cap, but you’ve decided to investigate the buried city to see if there are clues to how their civilization survived on a desert planet. The city is mostly ruins except for three intact pyramids— two open and one sealed. In the first you find a series of symbols and pictograms, revealing a fortuitously base 10 numbering system.
The second pyramid’s facade is covered in these symbols. Inside you discover a device, as well as mosaic representations of how to use it.
From those you glean the following: the device is the key to opening the sealed pyramid by inputting the number on the center block. But if you put in the wrong number, something terrible and deadly will happen. The doors to all pyramids work on the same principle.
What number should you input to open the door to the sealed pyramid?
Pause here to figure it out yourself. Answer in 3
Answer in 2
Answer in 1
The pattern revealed by the second pyramid is that every number is the sum of the two numbers directly beneath it. If that applies to the sealed pyramid, 40 clearly belongs to the left of 30. The center number is the sum of 7 and an unknown, call it x. The value of x can be determined by trial and error, but it’s quicker to use algebraic reasoning. The number to the left of the center number is 5+x. Therefore, this block, 40, is equal to 5+x plus 7+x. Solving for x, x must be 14, making the central block 21.
You enter 21 on the remote, and the door opens!
Inside you find yet another riddle. The walls show the history of this civilization.
When they lived here, the planet was covered with oceans. But at a certain point, they up and left Mars. In order to reserve the planet for themselves while making it inhospitable to others, they moved all the water underground, using a gigantic engineering marvel activated by a single lever. The lever is hidden in the Great Pyramid. Pulling the lever again would reverse the process, and bring the water back to the surface.
But where is this Great Pyramid? The mosaics indicate it should be right here, but it’s clearly not. Without it, you have no choice but to climb back out of the city to the surface. And that’s when you see it. The city is the final pyramid, or at least one face of it. A great pyramid, indeed!
The city’s architects must have designed each district to show a number when viewed from above. But only these three survived the ravages of time. The key once again must be whatever number was in the center plaza. You rush there, but what number should you input into the remote?
Pause here to figure it out yourself. Answer in 3
Answer in 2
Answer in 1
You could write out the algebra again, but here’s a more visual approach.
Sketch a pyramid, and enter the known numbers. Between the 9 and the 10, you can put colored dots to represent the two unknowns at the bottom. Working your way up the pyramid and drawing the sums as you go will reveal that 100 = 19 + 3 green dots + 3 orange dots. So 3(green + orange)=81, and green + orange, which is the middle number, must be 27. You don’t actually have to figure out what green and orange are— in fact, they have a number of possibilities.
When you enter 27, a hidden mechanism opens in the middle of the plaza, revealing a staircase. You descend, and finally find yourself in a room with a giant lever in the middle. Only one question remains: do you pull it?
