July 2019 Puzzles
2. If one and a half hens lay one and a half eggs in one and a half days, how many eggs does one hen lay in one day?
1.  Mac has a certain number of students in his class.  If there had been as many students again as there actualy were in the class, plus 1/2 as many more, plus 1/3 as many more, plus 1/6 as many more, plus 8 more students, there would have been 170 students.  How many students were actually in the class?
5.Seamus likes to think of puzzles for his older brother.  His most recent one is this:  I have an apple, a tangerine, and a peach.  I weighed them two at a time, getting weights of 14 ounces, 18 ounces, and 20 ounces for the three possible pairs of fruit.  How much will each of the three pieces of fruit weigh?
4. a.  It is a six-digit decimal number.
    b.  Each of its digits is a square number.
    c.  It is a palindrome.
    d.  Its hundredth digit is a divisor of each of its digits.
    e.  The least common multiple of its tenth digit and its thousandths digit is 36.
    f.  Its square root is greater than 30.
6.   A calculator that cost $150 is reduced by 40% for a special weekend sale.  By what percent must the special sales price be increased to bring the price back to $150.
3.  a.  It is a four-digit whole number.
     b.  It is greater than 4000.
     c.  the sum of its hundreds digit and its ones digit is 9.
     d.  Twice its tens digit is 2 more than its thousands digit.
     e.  The sum of one-fifth of its hundreds digit and two-thirds of its ones digit is 6.
     f.  Its tens digit is 1 less than its thousands digit.