Good to see so many people actually trying out puzzles I posted. Seeing more than 600 hits in 5 days(200 on Sunday) was quite impressive.
Thanks for the suggestions especially regarding the last two posts. For many of you those were very easy puzzles but main motive behind those was to get away from the mathematical point of view and think in a slightly different way. So, if those are easy, then lets solve some easy puzzles.
Some also asked about the solutions of the puzzles I have posted. To solve that problem, I will request the puzzle solvers to put your solutions on the blog rather than discussing it on the chat with me. This way, many people might benefit from your solutions and also, I won't have to write all the solutions by myself.
Here are few more puzzles. Have fun solving puzzles!
1. In a rectangle that's 2 by 200 units long, it's trivial to draw 400 non-overlapping unit-diameter circles. But in the same rectangle, can you draw 401 circles? (non-overlapping, unit-diameter.)
2. Two fathers took their sons to a fruit stall. Each man and son bought an apple, But when they returned home, they had only 3 apples. They did not eat, lost, or thrown. How could this be possible?
3. If F(n) denotes the nth Fibonacci number. Then, prove that F(k*n) is a multiple of F(k).
Please leave your solutions as comments. Thanks!
2. possible only if one father was also a son, therefore is was grandfather, father and son.
ReplyDeleteQ1: Use triangular packing instead of square packing. I think this works.
ReplyDeleteQ3: F(n)=(a^n-b^n)/sqrt(5) where a and b are roots of the quadratic x^2=x+1. Your result follows.
triangular packing wont work. you add only 3/2 circles in an area of 2xsqrt(3)
ReplyDelete