Necklaces

Last Question:

What is the difference between the red letters and the black letters?

H F O J I G X L

Answer:

The black letters are the capital letters that have both horizontal and vertical symmetry. The red letters are asymmetrical.

Today’s Problem:

You task is to place seven beads on a necklace. Five of the beads are red and two are green. How many different necklaces can be made using the five identical red beads the the two identical green beads?

Letter Differences

Last Question:

There are 22 gloves in a drawer: Five pairs of red gloves, four pairs of yellow gloves and two pairs of green gloves. If the lights are out and you must select the gloves in the dark, how many must you choose to ensure that you have at least one matching pair?

Answer:

If the drawer contained socks, then you would need to select only four to get a matching pair. But gloves have an attribute that socks do not have, the attribute of handedness. There is one glove for the right hand and one glove for the left hand.

It is not enough to have two gloves that are the same color. They must be of complementary handedness. To ensure that you have one pair of gloves, you must select one more than the number of gloves of one handedness, or twelve.

Today’s Question:

What is the difference between the red letters and the black letters?

H F O J I G X L

How Many Gloves Does it Take?

Last Question:

Your friend George gives you the following argument about coin tossing:

The odds of three tossed coins turning up all heads or all tails is one in two, that is 50-50. That is because anytime you toss three coins, at least two must match, either two heads or two tails. So that means the third coin – which is equally likely to be heads or trails, determines the odds.”

Is your friend George right? If not, what are the odds of three tossed coins turning up all heads or all tails?

Answer:

I am afraid George is dead wrong. The odds for each coin are independent of the others. There are two possible outcomes for a singe coin. I  found possible outcomes for two coins and eight possible outcomes for three coins:

Coin 1 Coin 2  Coin 3

H H H
H H T
H T H
H T T
T H H
T H T
T T H
T T T

In only two tosses out of eight will the coins land all heads or all tails.

Today’s Question:

There are 22 gloves in a drawer: Five pairs of red gloves, four pairs of yellow gloves and two pairs of green gloves. If the lights are out and you must select the gloves in the dark, how many must you choose to ensure that you have at least one matching pair?

Three Coins

Question:

Say the first six words of Lincoln’s Gettysburg address

Answer:

Four score and seven years ago …

Today’s Question:

Your friend George gives you the following argument about coin tossing:

The odds of three tossed coins turning up all heads or all tails is one in two, that is 50-50. That is because anytime you toss three coins, at least two must match, either two heads or two tails. So that means the third coin – which is equally likely to be heads or trails, determines the odds.”

Is your friend George right? If not, what are the odds of three tossed coins turning up all heads or all tails?