Truffle Kerfuffle
The factory’s robotic truffle picker is making gift boxes with a single row of seven unique types of truffles. The assortment includes three white chocolate truffles, while the other four are milk or dark chocolate. The placement of the seven truffles in the row is completely random. What are the odds that a given gift box will have white truffes on both ends?
Cylinder Splendor
Shown below are 20 pneumatic cylinders, divided into groups of 6 and 14 and forming two enclosed shapes. The area of the larger shape is exactly 3 times larger than the smaller (the dashed line are shown only to help envision the sizes of the enclosures). Can you divide the 20 cylinders into groups of 7 and 13 and accomplish the same arraignment (i.e. create two closed areas with one area exactly three times larger than the other)?
Did you know that Automation Direct sells a full line of pneumatic components, including over 800 models of cylinders in seven popular styles: non-repairable, stainless-steel NR, compact, compact extruded, NFPA tie rod, dual guide rod, and ISO 1552. (https://go2adc.com/pneu)
Suction Cup Shuffle
Can you place 6 suction cups on a flat surface and then slide them into the exact arrangement shown? (feel free to use identical coins if you don’t have six suction cups at hand) The round objects must be positioned exactly, not “by eye”, and you may not lift any of them from the surface – or the solution would be trivial. No measuring or marking should be needed, you just need the six objects, and a clever method.
Did you know that Automation Direct offers a line of pneumatic vacuum products, including Schmalz suction cups, end-of-arm tooling components, vacuum ejectors and accessories? (https://go2adc.com/vacuum)
And yes – we’re aware that suction cups don’t slide very easily 😉
Answers Below!
.
.
.
.
.
.
.
.
Truffle Kerfuffle
Remember that all the truffles are unique. So there are 5040 possible arrangements of the seven truffles. That’s “seven factorial” (7!). And then there are six possible arrangements of the two white truffles on the ends with 120 possible arrangements (5!) of the remaining 5 middle positions – for a total of 720 arrangements (6 x 5! = 6!) with white truffles on both ends. So, there is exactly a 1 in 7 chance that any given box will have white truffles on both ends.
Cylinder Splendor
Here is one solution – again the dashed lines are simply to show some equilateral triangles that help envision the size of the enclosures (5 vs 15 triangles). There are many other solutions.
Suction Cup Shuffle
Start by positioning the six objects into two rows as shown. They will self-align if touching at these nine points:
Then move #4 to just touch #5 and #6 (without bumping them out of their positions).
Then carefully slide #5 out of the central location and move it to just touch #1 and #2 (again without bumping the others)
Now, simply move #1 around until it just touches both #4 and #5. Viola!
