IMO 2018 Shortlist C4
An anti-Pas al pyramid is a nite set of numbers, pla ed in a triangle-shaped array so that the rst row of the array on...
Category: Combinatorics
Problem
An anti-Pas al pyramid is a nite set of numbers, pla ed in a triangle-shaped array
so that the rst row of the array ontains one number, the se ond row ontains two numbers,
the third row ontains three numbers and so on; and, ex ept for the numbers in the bottom
row, ea h number equals the absolute value of the dieren e of the two numbers below it. For
instan e, the triangle below is an anti-Pas al pyramid with four rows, in whi h every integer
from 1 to 1 2 3 4 “ 10 o urs exa tly on e: 2 6 5 7 1 8 3 10 9 . Is it possible to form an anti-Pas al pyramid with 2018 rows, using every integer from 1 to 1 2 ¨¨¨ 2018 exa tly on e?
(Iran)