Can You Guess the Secret Word in This Brain Teaser?

On his YouTube channel Mind Your Decisions, Presh Talwalkar shares logic puzzles dealing with geometry, statistics, and algebra. The puzzle below from the former Stanford math and economics student features no numbers, but that doesn’t mean it's easy to figure out.

To solve the brain teaser, you need to guess the secret word based on a few clues. Here’s the set-up: A teacher is leading a class and Albert, Bernard, and Cheryl are his students. He writes the words "cat," "dog," "has," "max," "dim," and "tag" on the board. He distributes one sheet of paper to each of his three students, with each piece containing a different letter from one of the words. He then tells them that together their letters spell one of the words on the board. The students only know their letter, they don’t know anyone else's.

The teacher asks Albert if he knows the secret word. Albert says yes, he does know it. Next, the teacher asks Bernard. After some hesitation, he replies that yes, he knows the secret word as well. Finally, the teacher asks Cheryl if she knows what the word is. She thinks for a moment and says that yes she does. Albert, Bernard, and Cheryl have successfully guessed the secret word. Do you know what it is based on their answers?

Figuring out the word without knowing any of its letters may seem difficult, but it’s not impossible. If you don’t know where to start, think about Albert’s answer and use the process of elimination to rule out some of the letters and words written on the board. Keep in mind that Bernard could only come to his conclusion from Albert’s answer, and Cheryl from Bernard’s.

Still lost? If you haven’t gotten to the bottom of it yet, the correct answer is "dog." When Albert answers that he knows what the right word is based on one letter, you can use that information to narrow down his possible letters to one of the six that are never repeated on the board: c, o, h, s, x, and i. And when Bernard says that he knows too, you can deduce that his list of potential letters is limited to t, g, h, or s. That leaves "cat," "dog," and "has" as the three remaining options. Cheryl’s answer confirms that she has the letter d, which means the secret word is "dog."

If you’re looking for a more detailed walkthrough of the puzzle-solving process, check out the video from Presh Talwalkar below.

[h/t Mind Your Decisions]