PLAYING CARDS

Ivan built houses from playing cards. The picture shows the houses that Ivan built, a one-story house, two-story and three-story. How many cards does he need to build a four-story house?

Solution:

To know how many cards are needed for a 4 story house we need to use this formula: n∙(3∙n+1)/2

For example:

First story: ��⋅��+ �� �� = �� �� =�� cards

Second story: 2(3⋅2+1)/2 = 2⋅7/2 = 14/2 = 7 cards

Third story: 3(3⋅3+1)/2 = 3⋅10/2 = 30/2 = 15 cards

And now for the fourth story: one-story=2 cards two-story=7 cards threestory=15 cards

Explain your solution !

Marko Zalović, Technical School Virovitica, Croatia