# Mathematics Exploration Problems (IMSO 2005)

International **Mathematics and Science Olympiad** (IMSO) for Primary School 2005

1. The following figure shows a road map of the Gotthem City. Every road is one way, as indicated by the arrow.

Questions:

(a) [1 point] How many possible routes are there from A to D?

(b) [2 points] How many possible routes are there from A to H?

(c) [3 points] How many possible routes are there from A to L?

2. There are some people playing a card game. On the table there are fifty cards, numbered 1 to 50, all facing up. Each player is allowed to choose a certain number of cards. If the sum of the numbers on all the cards chosen by the player is the highest, then he/she is the winner. There is only one winner.

Questions:

What is the lowest possible score that makes a player a sure winner if each player has

to choose:

(a) [2 points] two cards?

(b) [2 points] three cards?

(c) [2 points] five cards?