Hints for Professor Tangent's Brainteasers

Divide and conquer works for this type of problem. Divide the problem into simpler steps, and then assemble the simpler steps into a final solution.

First consider 2 balls - one blue, the other red, the 10 other being white and the same weight. Balance the red ball against any white ball. If they balance, the blue ball is different, but you still need another balance to determine if it's lighter or heavier.

Now consider 3 balls - one blue, one red, one green, the 9 others being white and the same weight. You could balance the blue, red and green balls against any 3 white balls, which tells you if the different ball is lighter or heavier. You could balance the blue and red balls against any 2 white balls. If they balance, the green ball is different. If they don't balance, you at least know if you're looking for a lighter ball or a heavier ball. If you previously determined either the red, blue or green ball is heavier, balance the blue ball against the red ball. If they balance, the green ball is heavier.

What difference does it make?

What is half a hole?

"On" and "off" status alone doesn't provide enough information. What other properties of a switch or light might be helpful?

Start with the clues that are independent from everything else. A few more will follow from these. Once the "easy" clues are used, look for clues with only 2 possible solutions. Try to eliminate one of the 2 possibilities by looking for a contradiction with other clues. Once you have 4 columns filled in, you also know the contents of the 5th column.

What values are necessary or impossible? How can the sum be 5 digits if the numbers added only contain 4 digits each?

How many possible interpretations are there for the words and phrases within the question?

How many ways can both containers be used together?

Which observations determine how many individuals are involved?

What would allow Rudy or Trudy to deduce their hat's color?

A simple question, such as "which road leads to T-town" is not very helpful since you don't know whether the answer is the truth or a lie. A more complex two-component question would be more helpful, perhaps involving either the truth about a lie, or a lie about the truth. Either way, the final answer is a lie. Another possible approach would be to find a question that T-towners and F-towners would answer differently if both actually told the truth. Since F-towners actually lie, the final answer would be the same either way.

At the market determine which comments must be false, or cannot be true.

When determining which suspect really did it, remember that only 1 speaks the truth. Which statements must be true, or cannot be true?

When measuring cold, what are we really measuring and how do we measure it?

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