May 20
​1.  The Algenauts baseball team just finished a great year.  During the season, they won three out of every four of their home games and two out of every three of their away games.  All together they won 40 more games that they lost.  If they played as many home games as away games, what was their final record of wins and loses?
​2. In the playoffs, the Algenauts won their division playoff series 3 games to 1 and then beat their arch-rivals the Geometers in the League Championship series 4 games to 2.  If the Algenauts won 80% of their home playoff games and 60% of their away playoff games, what percentage of their playoff games were at home?
​3. I'm thinking of a particular integer.  It is a multiple of three, five, and seven.  No digit occurs more than once.  Can you find my number?
    With that information there are lots of possibilities, so let me narrow the problem down with a few more clues.
  •     The digit in the tens place is a square number.
  •     The digits in the hundreds place is a cube.
  •     The digit in the hundred thousands place is both a square and a cube.
  •     Only the digit in the hundreds place is larger than the digit in the ones place.
​5.  Write the numbers 71 through 80 using exactly six five's.  You are allowed to use any mathematical symbols you know.
​4.  What is it that, after you take away the whole, some still remains?