Riddle from Amsterdam

Here is a spicy riddle from Bugra from Amsterdam:

A tortoise is walking home to his well deserved piece of lettuce after his long working day. The distance to its home is 10 km. Since tortoises aren't usually in a hurry, he decided to take a five-minute break after walking half of the distance. The tortoise repeats this: each time it has walked half the remaining distance it takes a five minute break before continuing.

Will this tortoise ever get home? Explain your answer!


  1. This reminds us of Zeno's paradox. Zeno was an ancient philosopher who lived 2.500 years ago. A paradox is a statement seemingly contradictory to common sense yet perhaps true (I searched the Miriam Webster on-line!)
    For example you want to reach a room. First you have to cover half the distance to reach it. Then you have to cover half of the remaining distance. Then you do the same to eternity and you never get there!!
    Find more in
    Nikos and Lefteris from the Pomegranate team

  2. The tortoise has to walk the distance D=10 km.
    I. It walks: Dx1/2 and take a break
    II. It walks: (D x 1/2) x (1/2) = D x (1/2) x (1/2)
    III. It walks: (D x 1/2) x (1/2) x (1/2) = D x (1/2) x (1/2) x (1/2)
    . . . . . . . . .
    n. It walks (D x 1/2) x ..... x (1/2) = D x (1/2) x ..... x (1/2) ; n belongs to N

    So the tortoise has to walk D/2 by n times and then it takes a break.
    N has an infinite elements. So D x (1/2) x ..... x (1/2) is infinite.
    The tortoise has to take an infinite number of breaks.
    The tortoise never arrives home.

    This problem is very funny and interesting.

    Mihnea Vonica,
    From Bucharest, Romania

  3. What Mihnea (who, by the way, is the group's Mathematician!)wants to say is that the number of fractions that have as denominator powers of 2 is infinite, therefore the number of breaks will be infinite. I hope I got you right, haven't I, Mihnea?
    Well, Bugra, is his answer correct?

  4. Hi everybody, sorry that I'm answering so late...
    I've seen your comment (calculation) and it's all correct. I didn't know that someone would give such an answer. And your answer is also correct, "The tortoise >>>never<<< arrives home"!
    Thank you for your comment Mihnea.

    See you later,

    West-Amsterdam, The Netherlands