Mar/Apr17 BTs-Solutions, Solvers, etc.

Mar/Apr17 Brain Teasers – SUMMARY

REMINDER: Answers in red.  Solvers (submitted/correct) in blue. (Forgive any omissions.) Comments in green. For further elaboration, feel free to ask! 

1.  Harvey owes Sam $27.  Sam owes Fred $6 and Albert $15.30.  If, with Sam’s permission, Harvey pays off Sam’s , debt to Albert, how much does he still owe Sam?  Several folks asked good questions here.  I finally decided the thing is/was worded too ambiguously and gave credit to all submitters.  🙂 
2. If the second half of the last name of our first president contains the second letter in cheese, then list (as your answer) the second word in this sentence.  Otherwise, list the first word in this sentence. “Otherwise”.  Jim Waterman, Amy Ragsdale, Anita Dixon, Alexis Avis, Rita Barger.
3. Consider this set of numbers:  { 0.66, 0.088, 0.7 }.  Find the difference between the smallest and largest these numbers and list this answer as a fraction in lowest terms.  153/200   Amy Ragsdale, Anita Dixon.
4. There are two integers whose squares that are 20 greater than than the integer itself.  Find ONE of them.  Both 5 and -4 share this property.  Jim Waterman, Amy Ragsdale, Anita Dixon, Alexis Avis, Rita Barger.
5. Tuesday (3/14) was PI DAY!!  (And also Einstein’s birthday 🙂 ).  Which is a better approximation (as in closer to actual value) for pi –  3.14 or 22/7?  22/7 is closer.   Amy Ragsdale, Anita Dixon, Alexis Avis, Rita Barger.
6. Find the sum of the reciprocals of the prime factors of 60.  31/30.    Amy Ragsdale, Anita Dixon, Alexis Avis, Rita Barger.
7. 0.1 + 0.2 – 0.3 x 0.4 / 0.5 = ?  .06  Amy Ragsdale, Anita Dixon, Alexis Avis, Rita Barger.
8. If the first ten counting numbers are put in a hat and one is drawn at random, what is the probability of drawing either a prime or a square?   7/10.      Jim Waterman, Amy Ragsdale, Anita Dixon, Alexis Avis.
9. The integer 6, say, has 4 whole-number divisors: 1,2,3,and 6.  What is the smallest number with exactly FIVE whole-number divisors? 16.   Amy Ragsdale, Anita Dixon, Alexis Avis, Rita Barger.
10. Suppose a person has a pulse rate of 72 beats/minute.  How many times will his/her heart beat in April? 3,110,400 times.   Jim Waterman, Amy Ragsdale, Anita Dixon, Alexis Avis, Rita Barger.
11. Leo made a list of all the whole numbers from 1 to 100.  How many times did he write the digit 2?  20  Amy Ragsdale, Anita Dixon, Alexis Avis, Rita Barger.
12. An integer between 44² and 45² has a factor of 5², and is a multiple of 13.  What is the number? 1950  Amy Ragsdale, Anita Dixon, Alexis Avis, Rita Barger.
13. How are the following numbers arranged?  2  3  6  7  1  9  4  5  8 They are listed in reverse alphabetical order, by spelling.  Jim Waterman, Amy Ragsdale, Anita Dixon, Rita Barger.

BONUSES

B1.  (carried over) What is the only year (last two digits) each century that has seven (7) Year-Product Days*? [2]  ’24  Anita Dixon, Rita Barger.
B2.  (see #4 above) Find the other integer whose square is 20 more than the number itself. [2]  See #4 above.  Jim Waterman, Amy Ragsdale, Anita Dixon, Rita Barger.
B3.  Counterfeit Coin #3  A new twist of Jan/Feb’s problems (but easier than that bonus!!).  You now have 18 coins.  You know one of them is counterfeit – and that it is slightly heavier than the good coins, and you still have your balance scale. Determine the bad coin, still with only 3 weighings.  (A ‘weighing’ consists of coins being placed on both sides.) [2] There are at least two approaches to this one.  (See them both below).  Rita Barger.
B4.  (see #9 above) What’s the smallest number with exactly SEVEN (7) whole-number divisors?   [2]  64  Anita Dixon, Rita Barger.  (Amy Ragsdale submitted 729 which is the second smallest such number [and cool in/of itself!], but not the smallest.)
B5. (see #11 above)  Same question for a list from 1 – 1000. [2]  300.  Anita Dixon

*Days whose month*day = year (last two digits)

Rita Barger’s solution to B3:  Divide into 3 piles of 6 and weigh 2. If they balance you know the other pile has the heavy coin. If they don’t balance select the pile that is heaviest. Take the identified pile of 6 and divide it into 3 piles of 2. Weigh 2 of them and determine which of the 3 piles is the heaviest in the same manner as the first weighing. Take the identified pile of 2 and put one on each side of the balance. It will show the heavy coi

Another approach: Split the coins into two stacks of 9 and weigh them.  Take the heavier pile and split them into 3 groups of 3.  The second weighing will then determine the heaviest of those piles.  Take the final 3 coins and put 2 of them on scale – the heavier is the counterfeit (OR, if they balance, the one left off.)