**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! **

- 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. 🙂** - 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.** - 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.** - 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.** **Tuesday****(3/14) was PI DAY!!**(And also Einstein’s birthday 🙂 ).**22/7 is closer.****Amy Ragsdale, Anita Dixon, Alexis Avis, Rita Barger.**- Find the sum of the reciprocals of the prime factors of 60.
**31/30.****Amy Ragsdale, Anita Dixon, Alexis Avis, Rita Barger.** - 0.1 + 0.2 – 0.3 x 0.4 / 0.5 = ?
**.06 Amy Ragsdale, Anita Dixon, Alexis Avis, Rita Barger.** - 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.** - 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.** - 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.** - 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.** - An integer between 44
^{2}and 45^{2}has a factor of 5^{2},*and*is a multiple of 13. What is the number?**1950 Amy Ragsdale, Anita Dixon, Alexis Avis, Rita Barger.** - 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.)**