Mr. Adams left $1872 in his will, with the instructions that it was to be divided among his widow, 3 sons, and 2 daughters. The widow’s share amounted to 3 times the amount that either of the daughters received, and each son got just half as much as each daughter. Find out how much each person got.
Set 14
Checking Account Charges
The First Rank Bank charges me 10 cents per check plus 25 cents per month service charge for my checking account. Now they’re going to start charging me 8 cents per check plus 50 cents per month service charge. Should I be happy?
Fraction Sum
Twice a fraction plus half that fraction, all times that fraction, equals the fraction. What is the fraction?
Repeated Division w/Remainders
N is a positive integer.
When N is divided by 3, the quotient is Q_{1} with remainder 1.
When Q_{1} is divided by 4, the quotient is Q_{2} with remainder 1.
When Q_{2} is divided by 5, the quotient is Q_{3} with remainder 1.
If Q_{1}, Q_{2}, and Q_{3} are positive integers, find the smallest possible value for N that will make all of this work.
Louie’s Age (Squares)
Louie won’t tell you his age, but it happens that if you square his age this year, and you square his age next year, the difference between those two perfect squares is 75. So how old is he?
School Start Survey
A massive survey was conducted at school last week about changing the time school starts in the morning. Results indicated 415 of the 700 people said they’d be happy if school started later in the morning, 269 said they’d be happy if it started earlier, and 123 said they’d be happy either way as long as there was a change. How many people wanted no change at all?
Anastasia Birthday
One morning Anastasia said to me, “As of two days ago I was still 15 years old. Some time next year I’ll have my 18th birthday and I’ll turn 18 that day.” When’s her birthday, and on what day was she speaking to me?
Five Students in Contest (Lies)
Five students, Annie, Barbara, Chris, Don, and Eleanor, took first through fifth place in a contest, but not necessarily in that order. They were chatting with you about it afterward, and they made the following comments:
Annie: Don was third.
Barbara: Eleanor was not first.
Chris: I was not last.
Don: Chris was lower than Barbara.
Eleanor: Barbara was second.
The comments of those who took first and second place are false; those of the others are true. Who won what prize?
Digital Clock Sums
In exactly 12 hours, for how many minutes is the sum of the digits on an electronic digital clock greater than 15? (Use just the digits that give the hour and the minute.)
CryptProd: Digits Used Once 2
0  2  
x  3  


5 
In this multiplication problem, all of the digits 0 through 9 have been used exactly once. Can you fill in the blanks to make it true?