A logic problem by Victor Paes Plinio

Logic Level 3

Regina, Paulo and Iracema are trying to guess how many balls there are inside a box. They know that the number of balls is greater than 100 and lesser than 140.

They made these following statements:

Regina said: In the box there are more than 100 balls and less than 120 balls.

Paulo said: In the box there are more than 105 balls and less than 130 balls.

Iracema said: In the box there are more than 120 balls and less than 140 balls.

Only one of these statements are true. How many possible values for the number of balls inside the box?

Example: If in the box can only be 116 or 125 or 136 balls, you answer should be 3 because there are 3 possible values.


Problem from OBMEP 2005
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