Jovan managed to build five houses of cards using a total of 90 playing cards. Now, he is curious to see if he can build one large house consisting of exactly 100 cards. Is it possible to create such a house of cards? According to Amanda Montañez, and the source Hans-Karl Eder/Spektrum der Wissenschaft, it is indeed possible to build a house of cards with exactly 100 cards, and it would have eight floors.
To achieve this, the number of cards increases level by level in a constant sequence. In order to prove the answer to this puzzle, it is necessary to demonstrate that 100 is a term in this sequence. The consistent increase in the difference between terms—the “second difference” being constant—allows for the representation of the sequence, with the number of cards K and the number of rows x, through a quadratic equation in the form of K = ax2 + bx + c.
The next step is to determine the values for a, b, and c by using a system of three equations. Once these values are found and the value for K is calculated as 100, the quadratic equation can be solved. This will lead to discovering a natural number value for x, which will enable the construction of a house of cards with exactly 100 cards.
If you decide to take on this architectural math puzzle and build your own house of cards with 100 cards, don’t forget to share your experience with us! You can email us at games@sciam.com to tell us all about it.
This intriguing puzzle was originally featured in Spektrum der Wissenschaft and has been shared with permission for all the math and puzzle enthusiasts to enjoy.