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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 1

What day comes three days after the day which comes two days after the day which comes immediately after the day which comes two days after Monday?

 

Challenge 2

The sum of four numbers is 60. One of the numbers is 50% more than the sum of the other three numbers. What is the value of this number?

 

Challenge 3

A circle is circumscribed about a square (as shown below). A second circle is inscribed in the square. What is the ratio of the area of the smaller circle to the area of the larger circle? (Note: express your answer as a common fraction.)

 

 

 

 

 

 

 

 

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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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Last month's solutions

Calculate Maze

Begin at the key marked ‘START’ and carry out the calculation as indicated. Once you have got that answer, find that corresponding number on a different key. On that different key calculate its answer and with this new number proceed to the next key. Continue on in this way until you eventually find a number that does not lead anywhere else. What is that final numbered key?

Solution:

 

 

 

 

 

 

 

Boxed in?

A shipping service restricts the dimensions of the boxes it will ship for a certain type of service. The restriction states that for boxes shaped like rectangular prisms, the sum of the perimeter of the base of the box and the height of the box cannot exceed 130 inches. The perimeter of the base is determined using the width and length of the box. If a box has a height of 60 inches and its length is 2.5 times the width, what is the maximum width which is allowed for this box?

Solution:

 Given: box height =  60 inches

 Let x = maximum box width, in inches

 Then, box length = 2.5x

 Therefore,   2(2.5x + x) + 60 = 130

                                                 7x = 130 – 60

                                                  7x = 70

                                                    x = 10 inches (max. width)

What’s the angle?

In the figure below, RT = TU. What is the value of x⁰ ?

Given: Lines RT = TU

Triangle RTU is an isosceles triangle and angles 
TRU = TUR = (180 – 114)/2 = 33⁰

Therefore, x⁰ = 180 – 83 – 33 = 180 – 116 = 64⁰

 

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