The Altonian brain teaser was a puzzle that required the "player" to meditate, clearing one's mind from distractions and emitting theta waves. The player's success or failure is demonstrated by an iridescent sphere, and when his or her mind is completely clear, the sphere will become one solid color. The more distracted a player is, the more multicolored the sphere becomes, even vanishing entirely. (DS9: "A Man Alone")

The difficulty level varies according to species and other circumstances. Other than the Altonians themselves, Vulcans are the next most adept species (numerically speaking) to succeed at the brain teaser, followed by Cardassians. Glinn Bresul Yejain, for instance, was known to have solved the brain teaser in less than four years' time. On the other hand, Gul Tayben Berat has stated it is possible that he will never solve the puzzle due to his neurological condition. That said, his attempts at the puzzle do seem at times to temporarily reduce the incurable tremors that result from his injuries. Gul Berat even employed the Altonian brain teaser as part of a distraction for the Vorta "representative" aboard the Sherouk. (Star Trek: Sigils and Unions: "Let He Who Has Eyes See")

Jadzia Dax is another individual who has spent an extensive time attempting to solve the brain teaser, and at one point she convinced Julian Bashir to try.

It is possible, though it cannot be proven, that the interplay between Trill host and symbiont, and the resulting neurological "noise" (similarly to the faulty signals that cause Berat's tremors) is the reason the difficulty level was so great for Dax, who had been attempting the puzzle with various hosts for 140 years.

Different individuals and species seem to approach the puzzle in different ways--at least, when it comes to the meditative pose. Jadzia Dax, for instance, meditated in a sitting, cross-legged position with eyes closed. Gul Berat, on the other hand, preferred a Cardassian form, knelt with arms outswept.

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