brainteaser!

"Suppose you had eight identical balls. One of them is slightly heavier and you are given a balance scale. What's the fewest number of times you have to use the scale to find the heavier ball?"

don't google the answer and be a spoiler:(

disclaimer: i got answer in just under 20 min:cool:

3 times. Step 1 - weigh 4 balls per side. Step 2, take the 4 balls from the heaviest side, and weigh 2 per side. Step 3, take the 2 balls from the heaviest side, and weigh 1 per side.
 
another mind twister, solve at the peril of your ego:D

A shelf contains hardcover and paperback books, of either fiction or nonfiction. How many books are on the shelf?

(1) 2/3 of the books are fiction and 1/4 of the books are hardcover.

(2) Fewer than 30 books are paperback and more than 10 are nonfiction.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

C. Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient to answer the question asked.

E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

C. 36 books - non-fiction = 12, fiction = 24, hardcover = 9, paperback = 27

Initial equation -> 2/3f + 1/3nf = 1/4hc + 3/4pb
smallest common denominator is 12
Multiply by 12 -> 8f + 4nf = 3hc + 9pb doesn't match because 4nf < 10
Next common denominator = 24 -> 16f+8nf = 6hc+18pb doesn't match because 8nf <10
Next common denominator = 36 -> 24f+12nf=9hc+27pb matches because 12nf > 10 and 27pb < 30
Next common denominator = 48 -> 32f+16nf = 12hc +36pb doesn't match because 36pb > 30
 
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