In each issue of the Automation Notebook we feature a section of brainteasers. These are the brainteaser answers from Issue 26, 2013 of the Automation Notebook. The brainteaser questions are repeated in black. The answers to the brainteaser questions are highlighted in red with explanations. You can view the brainteasers from Issue 26, 2013 without the answers here: http://library.automationdirect.com/brainteasers-issue-26-2013
1. Penny Wise
Place six pennies on a flat surface. Can you arrange the pennies in the exact positions shown, such that – IF you placed a seventh penny in the middle – it would touch all of the original six. You may not lift any of the pennies from the surface or use any other items, pennies, or measuring devices to assist, nor is it necessary to depend on your eye for judgment.
Answer: Use the following steps.
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2. Cutting Corners
Can you cut the following shape into four identical pieces that will fit together to form a square?
Answer:
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3. Tankless Task
A shipping company with a poorly maintained fleet of trucks was hired to convey a large number of tanks from a factory to be filled at a chemical plant across town. They loaded an equal number of the empty tanks on each of their many trucks. But as the drivers prepared for departure, it was found that 10 of the trucks would not start. So the tanks were redistributed, with one additional tank being added to each of the remaining trucks. Once the tanks were filled at the crosstown location, the drivers discovered that an additional 15 of the trucks would not start. So once again the tanks were redistributed; this time adding exactly 3 more tanks to each of the working trucks than had originally been loaded on each truck at the beginning of this shipping fiasco. By some miracle, all of these remaining trucks made it back to the factory. How many tanks were there?
Answer:
•Let x be the starting number of tanks on each truck
•Let y be the starting number of trucks
•So the total number of tanks is = x times y
•After the first redistribution the total could also be expressed as (x+1)*(y-10)
•After the second redistribution the total could also be expressed as (x+3)*(y-25)
•Solving two simultaneous equations:
So, if the starting number of tanks on each truck was 9…
Then from 10x=y-10, we know there were y = 90+10 = 100 trucks to start with…
And therefore a total of 900 tanks.
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4. Cable Cobble
Four professors, each with one of their students, went to purchase some flexible multi-conductor control cable. Each professor bought twice as many feet of cable as their respective student, and each person bought exactly as many feet of wire as the number of dollars he/she paid per foot of cable. Prof. Jones spent $76 more than Prof White; Nancy bought 3 feet less than Prof. Brown; Glen bought 2 feet more than Hal, who spent $48 less than Prof. Smith. What is the name of Mary’s Professor?
Answer:
Mary’s Professor must have been ‘Jones’.
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