chris11
Well-known member
Hey, one of the things that I do when I'm anxious is try to distract myself by playing with some puzzles, either of my own design, or someone else's.
Here are a few:
1. Take an 8x8 chess board, cut off 2 oposing corners. Is it possible to tile the resultant board using 2x1 dominos? If this is too easy, is this possible with blocks that look like:
0
0 0 0? This didn't come out the first time, it shouldn't be an L shape, but do it with that way anyways. Then see if it's possible for a shape that has the 0 on the top of the 3, but over the central 0.
2. Def'n: A pair of natural numbers (a, b) is called a set of twin primes iff a and b are both primes and b=a+2.
i) Is it possible for a pair of twin primes to have diffrent digit lengths (number of digits)
ii) Is it possible (and, if so, when) for twin primes to have diffrent digit lengths in a base other than 10? For instance, can this occur in binary? Hexidecimal? 5? 2^n-1?
3. (something a bit more technical, yet sort of beautiful)
Find an open form summation for the nth derivitive of the product of 2 n-differencible functions f, g. (If you know it, TRY NOT TO USE INDUCTION: there is a better way!!!).
Here are a few:
1. Take an 8x8 chess board, cut off 2 oposing corners. Is it possible to tile the resultant board using 2x1 dominos? If this is too easy, is this possible with blocks that look like:
0
0 0 0? This didn't come out the first time, it shouldn't be an L shape, but do it with that way anyways. Then see if it's possible for a shape that has the 0 on the top of the 3, but over the central 0.
2. Def'n: A pair of natural numbers (a, b) is called a set of twin primes iff a and b are both primes and b=a+2.
i) Is it possible for a pair of twin primes to have diffrent digit lengths (number of digits)
ii) Is it possible (and, if so, when) for twin primes to have diffrent digit lengths in a base other than 10? For instance, can this occur in binary? Hexidecimal? 5? 2^n-1?
3. (something a bit more technical, yet sort of beautiful)
Find an open form summation for the nth derivitive of the product of 2 n-differencible functions f, g. (If you know it, TRY NOT TO USE INDUCTION: there is a better way!!!).