Math Puzzle: Play as an Architect in a House of Cards

You can build a house on the sand with exactly 100 cards. It will be an 8-story building.

The number of cards increases with each level in a fixed order. If we want to prove the answer to the puzzle, we need to prove that 100 is a term in this sequence.

Since the differences between the terms always change by the same amount (the “second difference” is constant), we can conclude that the sequence with the number of cards K and the number of rows is: ×can be expressed as a quadratic equation of the form: K = ax² + bx + c.

First, determine the following values: a, b and c. This can be achieved using the following three systems of equations:

Using the values ​​found, a, b and c The value calculated as K = 100, we can solve the quadratic equation.

one of the values ​​of × is the natural number for which you can build a house on the sand from exactly 100 cards.