**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.

*Rollin’ Down The River*book, which is due out in mid June.

- 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?
- 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. - 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. - There are two integers whose squares that are 20 greater than than the integer itself. Find ONE of them.
**Tuesday****(3/14) was PI DAY!!**(And also Einstein’s birthday 🙂 ).- Find the sum of the reciprocals of the prime factors of 60.
- 0.1 + 0.2 – 0.3 x 0.4 / 0.5 = ?
- 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?
- 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?
- Suppose a person has a pulse rate of 72 beats/minute. How many times will his/her heart beat in April?
- Leo made a list of all the whole numbers from 1 to 100. How many times did he write the digit 2?
- An integer between 44
^{2}and 45^{2}has a factor of 5^{2},*and*is a multiple of 13. What is the number? - 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)

1. $11.30

2. Otherwise

3.

4. 5×5=25

5. Answer is 3.14

22/7=3.142857

Pi=3.14159

3.14-

3.141857=0.002857

3.14-3.14159=0.00159

B1. Answer ’24.

1-24

2-12

3-8

4-6

6-4

8-3

12_2

B2. -4

-4×-4=16

16+ -4 = 20

B2. Correction 16 + absolute value of -4 = 20

10. 3,214,080 beats 72x60x24x31, that is entirely possible if the person has a fixed-rate pacemaker. Just think how much energy it takes for the heart to beat more than 3.2 million times. The heart uses 3,565,000 Joules of energy every 31 days. 118,000 is the energy output in 1 day and that is the equivalent energy generated by a 75 Kg man falling 550 feet.

1. If, by “with Sam’s permission” you mean that it would reduce Harvey’s debt, he would owe him $11.70. Otherwise, he still owes him $27.

2. Otherwise

3. 0.7 – 0.088 = 0.612

= 153/250

4. one of the integers

is 5

5. 22/7 is closer

6. (1/2)+(1/3)+(1/5) =

1 1/30

7. 0.06

8. 7-10

B2. the other integer

is -4

These are answers I got. Some answers may be crazy but maybe some are reasonable.

1. Guess he still owes $27. Didn’t say debt pay-off went against his own debt.

2 Otherwise

3. 301/5000

4. 5

5. 22/7 is better app

6. 1 1/30

7. 0.06

8. 7 out of 10 or 7/10

9. 16

10. 3,110,400 times

Didn’t have time to try bonuses.

Don’t try to figure out how or why I missed the ones that are wrong. If you got inside my head, it could be scary!!!

11. 20 2s

12. 1950

9. 16

10. 3,110,400 beats

11. 20

12. 1950

13. These are the single-digit counting numbers written in REVERSE alphabetical order.

B4. 729 has 7 factors

11. 2 is written 19 times, 2, 12, 22, 32, 42, 52, 62, 72, 82, 92, 20, 21, 23, 24 ,25, 26 ,27, 28, 29

13. The numbers are in descending alphabetical order.

B5. 2 is written 190 times, 10 × 19