Brainteasers — Issue 31, 2015

Fitting Splitting

Two engineers went to the AutomationDirect Web store and bought 30 NITRA pneumatic quick-disconnect fittings (some with chrome-plating, some without). As they discussed divvying up the cost, Fred pointed out that his portion of the order contained half of the chrome-plated fittings, but only one third of the plain fittings. He also declared (correctly) that his portion of the order totaled $27.

Four chrome-plated fittings cost the same as five plain fittings. How much was Wilma’s portion of the order?breakroom-teaser1

AutomationDirect sells pneumatic fittings at some of the lowest prices anywhere. We maintain excellent stock levels and have convenient package quantities for large or small orders. And take a hint from Fred and Wilma:  they spent more than $49 and thus qualified for our FREE two-day shipping!

 

ZipPort Assort Report

An eccentric customer called our Sales department recently and said “I have exactly $200 to spend on ZipPort Multi-wire Connector accessories. I need some Cable Glands ($1 each), ten times that many Couplers ($2 each), and fill the balance of the order with Threaded Adapters ($5 each)”.  Our sales staff took his order with no further information about the quantities required.  How many of each product did we ship?breakroom-teaser2

ZipPort heavy-duty multi-wire connectors are used wherever there is a need for secure, simple and time-saving connections within machinery and facilities. The connector housings are made of die-cast aluminum for all sizes (with metal or thermoplastic size 3A housings) and offer excellent protection against dirt, moisture and mechanical stress. Multi-wire connector inserts make it possible to easily connect signal, power, and data connections.

 

In a (lock) Box With a Fox

We installed one of those “wall-mount combination lock boxes” at our community center recently. It holds the key to the storage shed, and allows anyone who knows the code to remove the key from the lock box and open the shed. But it started a water cooler discussion amongst the engineers at the office as we debated the potential number of combinations. At first glance, it seems simple, there are 10 buttons (0-9) and the manufacturer recommends a four digit code (user-selectable), so the number of possibilities would be 10,000, right?  Not so fast … in this case, there are two extra rules:  Due to the mechanical nature of the lock, you can only use a given number once in your user-selected code AND this is the real kicker: order is unimportant. So code 1234 is the same code as 4321 or 4231.

So, what is the total number of distinct 4-digit combinations possible for this lock?breakroom-teaser3

Extra Credit: 

It turns out that the lockbox will accept codes of any length (although some lengths would seem foolish).

What is the number if you consider all of the other length combinations (i.e. 3-digit, 5-digit, 6 digit, etc.)?

 
— The first two puzzles are credited to Sam Loyd (1841 – 1911).  Apparently, he was quite the character:  http://en.wikipedia.org/wiki/Sam_Loyd 
 

Click here for answers