Cube to regular Hexagon

• How would you cut a plane through a cube, such that its intersection with the cube would be a regular hexagon?
  
  
  Read my next post for the Right Answer of this Question:
  
  
  
  
• Right Answer of the last asked Question is here:
  
  Tom and Britney were two long distance lovers. Tom lived in Chicago, and Britney lived in New York. Tom was eager to get married soon. Britney, who wanted to concentrate on her career, wanted to delay for at least two years. Knowing that Chicago and New York have a time difference on an hour, Britney told Tom over the phone that if he proposed at a time when both Chicago and New York have the same time, she would(may) agree to get married right away. Within a month, Tom proposed, and Britney agreed. And the married couple, at least for Tom, lived happily ever after. How did this happen? When did Tom propose?
  
  
  
  

  Tom proposed on the last Sunday of October. At 2 AM, in New York, the clock was set back one hour into the Standard Eastern Time. At Chicago, it was still Daylight Time, which ends an hour later. During this hour, both New York and Chicago has the same time.

  
  

  
  

  
  
  
  

Lovers how to Marry

• Tom and Britney were two long distance lovers. Tom lived in Chicago, and Britney lived in New York. Tom was eager to get married soon. Britney, who wanted to concentrate on her career, wanted to delay for at least two years. Knowing that Chicago and New York have a time difference on an hour, Britney told Tom over the phone that if he proposed at a time when both Chicago and New York have the same time, she would agree to get married right away. Within a month, Tom proposed, and Britney agreed. And the married couple, at least for Tom, lived happily ever after. How did this happen? When did Tom propose?
  
  Read my next post for the right Answer of this Question:
  
  
  
• Right Answer of the last asked Question is here:
  
  Angelina has 25 gold coins. One on those coins is lighter, while the rest of the coins have the same weight. If Angelina has a balance, how would Angelina determine which coin is the lighter one with 3 weightings?
  
  

  Divide the coins into 3 group consisting of 9 coins, 9 coins, and 7 coins. On the first weighing, weigh the 2 groups of nine coins. If they have the same weight, then the counterfeit is in the group with 7 coins. If one of the groups of 9's weighs less, then the counterfeit is on that group.

  On the second weighing, divide the group where Angelina knows the counterfeit coin is into 3 subgroups, where the first two subgroups would have 3 coins each. Weigh these first two subgroups. If they have the same weight then the counterfeit is on the third subgroup. If one of them weighs less, the counterfeit is on the subgroup that weighs less.

  Since the subgroup that contains the counterfeit has at most 3 coins. Weighing two of these coins will allow Angelina to know which coin is the counterfeit.