word prob

[dolor]

You have nine pearls--eight are real and one is fake. The real pearls all weigh the same, but the artificial pearl weighs less than the others. How can you find the fake pearl by using the balance scale twice?

[NotLKH]

Use the "Divide Group By 3, and weigh only 2 subgroups against each other" method, 2 times.

[pgrimes]

Split the pearls into 3 groups of 3. So, group1, group2 and group3 each consist of 3 pearls.

Next, put group1 and group2 on the balance. If the groups are equal, the fake is in group3 otherwise, the fake is in the lighter of the two groups on the balance.

Next, take either the lighter group or group3 (whichever contains the fake) and put two of the three pearls from that group on the each side of the balance. If they are equal, then the third pearl (the one not on the balance) is fake. Otherwise, the lighter of the two is the fake.

[pgrimes]

ya... what NotLKH said.

[NotLKH]

Good Explanation!