5 Logic problems to put your brain in work.

Below are listed several problems that need some logic to be solved.

1. MILK JUGS

A milkman has two empty jugs: a three gallon jug and a five gallon jug.

How van he measure exactly one gallon without wasting any milk?

2.SOCKS AND SHOES

You are in the dark and in the floor there are six shoes of three colors, and a heap of twenty four socks, black and brown. How many socks and shoes must you take into the light to be certain that you have a matching pair of socks and a matching pair of shoes?

3.TWIN BROTHERS

Suppose there are twin brothers; one which always tells the truth and one which always lies.

What single yes/no question could you ask to either brother to figure out which is which?

4.CUT THE CAKE

How is it possible to cut a traditional circular cake into 8 equal size pieces, with only 3 cuts?

5.FOUR DIGIT NUMBER

What is the four digit number in which the first digit is one third the second, the third is the sum of the first and the second, and the last is three times the second.

SOLUTIONS:

ANSWER 1: The milkman filled the three gallon jug, and then emptied the contents into the five gallon jug.  He                       then filled the three gallon jug again, and continued to fill the five gallon jug until it was full.  The                         milk remaining in the three gallon jug was precisely one gallon. 

ANSWER 2: Three socks and four shoes would guarantee that you would have a matching pair of each.  Since                       there are only two colors of socks, it doesn't matter how many are in the heap, as long as you                           take at least three, you are certain to have two of the same.  As for the shoes, you must pick                             four, because selecting only three could result in one shoe in each of the three colors! 

ANSWER 3: Answer: Would your brother say that you tell the truth? 

                      The key to this logic problem, is to find a question that the two brothers would answer differently,                       and that difference would therefore identify the two from each other.  The lying brother would                               answer the above question "yes."  The truthful brother would answer the same question "no." 

ANSWER 4: Make the first two cuts as cross-sections, making 4 equal pieces.  The third and final cut is                               made horizontally through the middle, making a total of 8 pieces.

ANSWER 5: 1349