Sunday Times Teaser 2999 – Triangular Card Tower
by Howard Williams
Published Sunday March 15 2020 (link)
Robbie leans two very thin playing cards together, then another two together, placing an identical card across the top forming a platform, and proceeding sideways and upwards to build a roughly triangular tower.
For the bottom layers, he uses a whole number of 53-card packs of large cards (integer length above 70mm), the number of packs equalling the number of bottom layers. He then uses small cards (75% size) to complete the tower, which is 1428mm high. The distance between the bases of two leaning cards is always 0.56 of the length of each card.
Robbie would like to extend the tower sideways and upwards to the next possible integer height, still using large cards only for the bottom layers.
How many extra cards would be needed in total?