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Posts posted by Morningstar

  1. I read about this in a Russian puzzle book and I don't think it's been posted before.

    A soccer goalie had just lost an important match, and when he went to sleep that night he had a strange dream. He dreamt that he was kicking a soccer ball against a wall, and as he did so, the soccer ball got bigger and bigger, and the goalie got smaller and smaller. Suddenly, the goalie turned into a ping-pong (table tennis) ball and the soccer ball turned into a massive hard exercise ball. The exercise ball rolled around, trying to crush the ping-pong ball. Without leaving the floor, is there any way the ping-pong ball can prevent being crushed?

  2. Your answer of noon and 400 days is correct

    Assuming you wear your Santa's hat on 12/25/2012, Christmas day, then your date is in error!

    is the fact that 2012 is a leap year, hence 366 days long.

    Pity...it would have been an interesting coincidence.

  3. By the way, is that number actually divisible by 23? I suppose that there's a 1 in 23 chance that any number is divisible by 23, but I wonder if there's some mathematical connection...

  4. I got that the number of numbers that their sum of digits is 23 is:




    Why aren't there an infinite number of numbers whose digits sum to 23? For example, if we take 6 as the number the digits sum to, the number 123 has digit sum of 6 but so do 1023, 1230, 1203, 10023, and anything else obtained by adding 0's.

  5. Design a track through the lands so that you cross each of the seven connections labeled, only once. All connections have to be completely traversed exactly once. The track must be uni-directional, i.e. you cannot double-back and move the way you came. (This one seems impossible)

    Assuming the labeled connections are the only ones, adding another bridge is the only way to solve it. This was first posed by the mathematician Euler in regard to the bridges of the Russian city of Königsberg.

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