Brain Teasers – Mar/Apr ’17

NOTE:  For any collection of FOUR (4) correctly solved BTs (there will be at least 12 BTs total), submitter will receive ONE entry into the drawing for a Rollin’ Down The River book, which is due out in mid June.

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?
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.
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.
4. There are two integers whose squares that are 20 greater than than the integer itself.  Find ONE of them.
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?
6. Find the sum of the reciprocals of the prime factors of 60.
7. 0.1 + 0.2 – 0.3 x 0.4 / 0.5 = ?
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?
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?
10. Suppose a person has a pulse rate of 72 beats/minute.  How many times will his/her heart beat in April?
11. Leo made a list of all the whole numbers from 1 to 100.  How many times did he write the digit 2?
12. An integer between 44² and 45² has a factor of 5², and is a multiple of 13.  What is the number?
13. How are the following numbers arranged?  2  3  6  7  1  9  4  5  8

BONUSES

All (legitimate) submissions to any of these Bonus BTs receive a entry into a drawing for the Rollin’ Down The River book when it is released.  All correct answers receive at least one more.  (Numbers at the end of each BT represent maximum possible entries to be awarded.)
B1.  (carried over) What is the only year (last two digits) each century that has seven (7) Year-Product Days*? [2]
B2.  (see #4 above) Find the other integer whose square is 20 more than the number itself. [2]
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]
B4.  (see #9 above) What’s the smallest number with exactly SEVEN (7) whole-number divisors?   [2]
B5. (see #11 above)  Same question for a list from 1 – 1000. [2]

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