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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.

## Challenge One

Items of fruit are sold singularly in a supermarket. From the information below can you list the seven fruits in order of price, starting with the most expensive?

A banana costs less than a peach but more than a pear, a kiwi costs less than a pear and more than an apple, a pineapple is more expensive than a peach and a lemon costs more than a kiwi but less than a pear.

## Challenge Two

You have 25 sticks standing upright in a circle, numbered 1 to 25. Starting with stick #3 and then rotating in a clockwise (CW) direction around the circle, knock over every other or second stick in each rotation of the circle (i.e., #4, #6, #8, etc). Keep rotating around and around the circle knocking over every second stick standing until only one stick remains standing. What will be the number of the last stick standing?

## Challenge Three The empty boxes contain any of the number 1-9, and no empty box contains the same number as another empty box.

The three numbers in cells D1-3 equal the value of the top row minus the bottom two rows’ values.

The three numbers in A4, B4 and C4 equal the value of the left most column minus the values of the other two columns

The same principle applies to the diagonal from A1 to D4
Solve the puzzle by finding all of the missing numbers that satisfy all of the results as shown.

## 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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## Challenge 1

While playing an arcade game, Tony comes across a hidden chamber that has been locked using a 5-digit password combination. Maura, the angel helping out the game character, gives the following hints:

1. The fourth digit of the password is four more than the second digit.
2. The third digit of the password is three less than the second digit.
3. The first digit is four times the last digit.
4. The sum of the third and fourth digits equal the sum of the fourth and fifth digits.
5. The total sum of the five digits equal 26.

Solution:

Let the five digits (1st, 2nd , 3rd , 4th & 5th ) be represented by (A, B C, D & E)

Given:

D = B + 4, C = B – 3, A = E * 4, C + D = D + E, or C = E
A + B + C + D + E = 26

Then:

(4E) + B + (B-3) + (B+4) + E = 26
4(C) + B + (B-3) + (B+4) + (C) = 26
4(B-3) + B + (B-3) + (B+4) + (B-3) = 26
8B – 14 = 26
8B = 40
B = 5

Therefore, D = 5 + 4 = 9, C = 5 – 3 = 2, E = C = 2, & A = 4E = 4*2 = 8

The password that opens the chamber is then 85292.

## Challenge 2

In each of the following set of calculations, there is a common arithmetic relationship between each that allow their respective solutions to be as shown. Determine this common relationship and find the unknown relational value in question.

1 + 4 = 5
2 + 5 = 11
3 + 6 = 19
5 + 8 = ?

Solution:

1 + 4 (*1-0) = 5
2 + 5 (*2-1) = 11
3 + 6 (*3-2) = 19
5 + 8 (*5-3) = 41

### Challenge 3

A perpendicular line is drawn from the top apex to the base in an equilateral triangle. The line is 3√3 inches in length. What are the perimeter and area of the triangle?

Solution: Let b = triangle’s base = √3 (½ * 3√3) = 4.5 inches

Using Pythagorean Theorem (a² + b² = c²) as a check of triangle values:

(½ * 3√3)² + (4.5)² = (3√3)²

6.75 +  20.25 = 27

Then, the triangle’s perimeter = 6 * 4.5 = 27 inches

And, the triangle’s area = ½ (2 * 4.5 * height) = 4.5 * (1½ * 3√3)

= 4.5 * 4.5 * 1.73  = 35 sq. inches