At 12 noon, the hour hand and minute hand of a clock are exactly on top of each other. How many more times will this happen before midnight?

On a train, Smith, Robinson and Jones are the fireman, brakeman, and engineer, but NOT respectively. Also aboard the train are three businessmen who have the same names: a Mr. Smith, a Mr. Robinson, and a Mr. Jones.

Mr. Robinson lives in Detroit.

The brakeman lives exactly halfway between Chicago and Detroit.

Mr. Jones earns exactly $80,000 per year.

The brakeman's nearest neighbor, one of the passengers, earns exactly three times as much as the brakeman.

Smith beats the fireman at billiards.

The passenger whose name is the same as the brakeman's lives in Chicago.

Question: Who is the engineer?

Assume all numbers involved are whole numbers

Fun fact: These types of problems, often referred to as “Smith-Jones-Robinson” problems, are a type of logic puzzle popularized by H. E. Dudeney in the 19th and early 20th centuries.

Every decision we make is shaped by a clear sense of purpose.

I came across a workbook with a long multiplication worked out. However, it uses a different script for the numerals and all I knew how to read is the numeral “7”, so I just wrote “N” for any numerals I did not know. Can you help me solve for the other numerals and fill out this multiplication exercise?

                        N N N

    x N N N N

    - - - - - - - - - - - - -  

      N N N 7

    N N N N 

  N N N N    

  N N N       

  - - - - - - - - - - - - - 

  7 7 7 7 7 7

Your mother’s co-worker has two children. One day she mentions that “her son was born in summer”. What’s the probability that her other child is a daughter?

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