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.
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:
- The fourth digit of the password is four more than the second digit.
- The third digit of the password is three less than the second digit.
- The first digit is four times the last digit.
- The sum of the third and fourth digits equal the sum of the fourth and fifth digits.
- The total sum of the five digits equal 26.
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 = ?
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?
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Last month's solutions
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?
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)
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
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?
|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