The Thinkers took the three time-travellers to separate rooms. Victoria greatly disliked being taken away from Jamie, but did her best to appear brave. They were taken to the rooms and placed inside, but each room was identical. Constructed of the same odd yet perfect geometry as the dome and the rest of the planet, with a small hexagonal pedestal in the centre, upon which rested a small white box.
The Doctor wasted no time in immediately examining the object, picking it up and inspecting it from all angles, poking and prodding it to see what it did. Upon a very close inspection, he ascertained that it was made up of numerous pieces which were all fitted tightly together, giving the illusory appearance of being completely. The Doctor 'hm'd and 'ha'd, until finally he pushed one block, and it slid clear of the others, revealing something black underneath the hard white substance.
He continued to slide more of the blocks away, realising soon that they were in a sequence of logic through numbers. 1-5, 2-5, 3-5, and so on. Eventually all the white pieces had fallen away onto the pedestal, revealing a smaller black box inside, which sat comfortably in the Doctor's hand.
Jamie, on the other hand, had begun by looking around the room, doing what he could to avoid the pedestal. The Doctor was always the one who did the thinking between them all. That was what he was good at. Jamie, upon inspecting the box, couldn't fathom it's usage at all. He picked it up and looked it over, but couldn't come to any sensible reasoning as to its purpose. Taking to his highlander roots and pounded the box hard against the pedestal, only for the box to suffer no apparent damage to either the box or the pedestal.
Jamie began prising at the box, sniffing it, biting it, and eventually proceeded to use every rude word in his vocabulary, even inventing several new ones in the process, but still the box refused to reveal its secrets to the Scot.
Victoria, like the Doctor, began by examining the box, but couldn't find anything about it worth noting or paying attention to. She was searching for some sort of indentation or groove, or any kind of mechanism which could aid in her accomplishing the puzzle. But the box was perfectly smooth at every point, even it's corners were rounded. She couldn't even understand what material it was constructed from, it was cold like metal, but smooth like plastic, yet strong as diamonds.
She too noticed that the box was made out of pieces, but wasn't aware what order they were to be pressed in. She managed to find the first option, but once it was pressed, she had to locate the other, and upon pressing the wrong one, the first slid back out, and Victoria had to locate it all over again.
At long last, the Thinkers returned to collect the trio, taking them back to the main hall. Jamie was brought in first, and once he saw Victoria entering, the two ran to see each other, making sure they were both alright. Then the Doctor entered, and joined the two, explaining how he had solved the puzzle.
Then the Thinkers took their place on the podium once more.
"Only one of you completed the challenge." The middle-most Thinker announced. "This is disappointing, but promising regardless. We shall proceed with our next test to further examine your mental processes."