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Each month, a new set of puzzles will be posted.  Come back next month for the solutions and a new set of puzzles, or subscribe to have them sent directly to you.

## Puzzle One

Ronald, Tony, Fiona, Paula and John have their birthdays on consecutive days, all between Monday and Friday.

• Tony’s birthday is as many days before Paula’s as Fiona’s is after Ronald’s.
• John is older than Fiona.
• Paula’s birthday is on Thursday.

Can you figure out whose birthday is on each day?

## Puzzle Two

Four playing cards, one of each suit (spades, clubs, hearts, & diamonds) face down on a table. They are a three, a four, a five, and a six.

1. The cards on either side of the four are black.
2. The club is to the right of the three but not next to it.
3. The spade is to the left of the heart.
4. The middle two cards add up to an even number. Neither of them is a club.

Can you determine the cards’ suits and their order?

## Puzzle Three

You’ve been invited to a party at Charlie’s house, but you’ve never been there. He has seven friends who live nearby. They’ve given you the following map showing all of their houses including Charlie’s house, along with the following information:

• Daniel: I can’t see Benita’s house, because Greta’s house is in the way.
• Adam: I live directly (not diagonally) across the street from Daniel.
• Benita: Elena lives due west of me.
• Elena: I have to cross three streets to walk to Franco’s house.
• Hal: I live east of Benita.

Can you figure out who lives where, and also which house is Charlie’s?

## Feedback

There are more than one way of doing these puzzles and may well be more than one answer.  Please let me and others know what alternatives you find by commenting below.  We also welcome general comments on the subject and any feedback you'd like to give.

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c)

## Puzzle One

In two years time my age will be three times the age of my son was two years ago. Three years ago my age was twice the age of my same son will be in three years time. How old are we both?

Solution:

Let x = my age and y = my son’s age

Given: (x + 2) = 3(y – 2); x + 2 = 3y – 6; x = 3y – 8

and (x – 3) = 2(y + 3); x – 3 = 2y + 6; x = 2y + 9

Combining the two equations for x:  3y – 8 = 2y + 9; 3y – 2y = 9 + 8

Therefore, y = 17 (my son’s age) and x = 3y – 8 or  x = 3(17) – 8 = 43  (my age)

Verifying results: x = 2y + 9 or x = 2(17) + 9 = 43

## Puzzle Two

There are 10 points equally spaced around the circle with interconnecting lines drawn between them.
a) How many lines are needed to draw the 10 point pattern shown below?
b) How many lines would you need if you had 50 points on the circle?
c) How many lines would you need if you had 100 points on the circle?

Solution:

Note: The following approach for counting the number of lines connecting the dots in a circle cans also be used for the number of individuals in a room shaking the hand with each of the other persons once.

a) Each of the 10 dots on the circle connects with 9 of the other dots or 10 x 9 = 90 lines. Since there are 2 points to every line, then the number of actual line is half of 90 or 45 total lines in the diagram. As an alternate approach, physical count them in the diagram.

b) If you now have 50 dots on the circle, each will connect with 49 of the other dots or 50 x 49 = 2,450 lines. Since there are 2 points to every line, then the number of actual line is half of 2,450 or 1,225 total lines in the diagram.

c) If you now have 100 dots on the circle, each will connect with 99 of the other dots or 100 x 99 = 9,900 lines. Since there are 2 points to every line, then the number of actual line is half of 9,900 or 4,950 total lines in the diagram.

## Puzzle Three

The missing numbers are between 0 & 9. The numbers in each row add up to the totals on the right, and the columns add up to the totals along the bottom. The sums of the diagonals are also given. Find the missing numbers? (Note: there may be more than one solution for each of these puzzles.)

Solutions: