OlympiadEasyCombinatorics7–9

A grasshopper starts at $0$ on a number line and makes $10$ jumps, each one unit to the left or to the right. How many different points can it end on?

Um gafanhoto parte de $0$ numa reta numérica e dá $10$ saltos, cada um de uma unidade para a esquerda ou para a direita. Em quantos pontos diferentes pode terminar?

Answer options

Solution

Step 1 of 3

1.After each jump the parity of the position flips, so after $10$ jumps the position is even.

A grasshopper starts at 000 on a number line and makes 101010 jumps, each one unit to the left or to the right. How many different points can it end on?

Answer options

A grasshopper starts at $0$ on a number line and makes $10$ jumps, each one unit to the left or to the right. How many different points can it end on?