Hauts : Tiling

TILING

You then head towards Kabul. After reaching there, you come to know that the King’s descendant found an ancient-Treasure Box. One of the men of the ancient court discovered that the code that unravels the treasure, is hidden in the below puzzles. Help the descendant and get 10% of the treasure as reward.

PUZZLE 1:

You are given ten ‘L’ shaped tiles of size 1 through 10. Stack tiles so that each tile is fully supported and also the stack is as high as possible. For example, we can stack L's of side 1 through 5 so that the stack is 18 units high and stack L’s of side 1 through 6 so that stack is 26 units high as shown in figures below.

[Note: It is not necessary that all the L’s should be present from one to 10]

Question 19:

What is the maximum height of the stack formed on stacking tiles of side 1 through 10?

And now, the shape of the stack gives you the shape of the key that unlocks the box but you still don’t know the size (in terms of number) of the key, which is hidden in the next puzzle.

PUZZLE 2:

A large square can be formed by small integer sided squares so that each square either lies on the bottom layer or lies on top of one or more larger squares. Some examples are shown below:

Question 20:

What is the smallest odd square that can be formed using above method?