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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

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.

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 = ?

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?

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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Last month's solutions

Challenge 1

A ship is battling against the tide to safety. It uses 7 gallons of fuel every hour and sails at 17 mph in still conditions. It is 77 miles from safety and the flow against it is 6 mph. The ship has 49 gallons of fuel left. Will it reach safety?

Solution:

Yes, but it will require all of the fuel available.
77 mi./ (17 – 6) mi/hr = 7 hr.
7 hr. x 7 gal/hr = 49 gallons (or equal to all of the fuel left)

 

Challenge 2

When 4 is added to two numbers, the ratio is 5:6. When 4 is subtracted from the two numbers, the ratio is 1:2. Find the two numbers.

Solution: The two numbers are 6 and 8.

Ratio 5:6 (A:B) (with 4 added)

Possible Numbers for A –   5    10    15    20     25    30

Possible Numbers for B –   6    12    18    24     30    36

Ratio 5:6 (A:B) (with 4 subtracted or original numbers prior to 5:6 ratio)

Possible Numbers for A –   1      6    11    16     21    26

Possible Numbers for B –   2      8    14    20     26    32

Ratio Original numbers – 4 (looking for ratio 1:2)

Possible Numbers for A –   2      7    12     17    21

Possible Numbers for B –   4    10    16     22    28

 

Challenge 3

An unknown airplane flying with a speed of 700 mi/hr is detected 1000 miles away by a radar. Half an hour later an interceptor plane flying with a speed of 800 mi/hr is dispatched. How long will it take the interceptor plane to meet with the unknown plane?

Solution:

Let x = the time it takes for the two planes to meet

(700 * x) + (800 * x) = 650

1500 x = 650 mph

x = 0.4333 hrs. or 26 minutes

 

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