A subtraction pyramid is a pyramid formed by non-negative integers, each of which is the difference between the two nearest numbers from the previous level (read from bottom to top). Here is an example of a subtraction pyramid:

## 1

2

2

5 7
4

3
5

8

A significant number is the largest number in the subtraction pyramid. An excellent pyramid is a subtraction pyramid that has a 0 at the top and at least one level consisting of distinct numbers.

1. How many levels must an excellent pyramid have at a minimum?
2. What is the smallest significant number that can be contained in an excellent pyramid with the minimum number of levels?

(K. Jasenčáková)

Hint. What does the level below the apex look like?
If it is 0 at the top, there must be two identical numbers in the previous row. Each excellent pyramid must have at least three floors.

An excellent pyramid with the smallest number of floors and the smallest possible numbers looks like this (except for the order of the numbers on the third line):

## 0

1

0 ..... 2

The largest number in this pyramid is 2, and that is also the answer to the second question in the problem statement.

Note. The top three floors of a subtraction pyramid with zero at the top look like this (except for the order of the numbers on the third line):

$$
b-a
$$

b

$b+a$

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