- Homer’s mother has four children. Three of the children are named Spring, Summer, and Autumn. What is the name of the 4th child?
- A man tossed a baseball 20 feet. It stopped in mid-air, reversed directions and came back to him. How can this be explained?
- [An old classic!] A brick weighs 3 pounds plus half (the weight of) a brick. How much does a brick and a half weigh?
- Find three consecutive
*odd*integers which are all prime. - You have a string of 10 consecutive integers. The sum of the first three is 39. What is the sum of the last 3?
- If x#y = x + y +7, then what is the value of (2#3) # (7#0)?
- I have twice as many nickels as dimes. If the value of my nickels is $5.00, what is the value of my dimes?
- My neighbor has four daughters and each daughter has exactly one brother. How many children does my neighbor have?
- What is the largest integer you can square and get an answer less than 3000?
- 1/19 is to 1/17 as what number is to 95?
- In the first quarter of a game, the Denver Nuggets missed only 7 of their 25 field goal attempts. What was their scoring percentage for that quarter?
- Simplify this expression: (99 – 9) x (99 – 19) x (99 – 29) x . . . x (99 – 199).
- In my hand, I have two US coins whose total value is 55 cents, but one of the coins is not a nickel. What are the two coins?
- A frog is at the bottom of a 30-foot well. Each day he is able to jump up 5 ft, but during the nigth, he slides down 3 ft. How many days will it take him to jump out of the well?
- “Brothers and sisters have I none, but this man’s father is my father’s son.” To whom is the speaker referring?

**BONUSES**

**B1. ****Counterfeit Coin #4** * Another* new twist of Jan/Feb’s problems. I am now convinced this problem can be solved with

**up to 27**

**coins(!).**So pick your own number(s) and solve: 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.)

**B2.** (see #4 above.) It turns out there is only one solution to #4 above. Why is that?

**B3. **(see #6 above.) If x&y = x # (y+7), then what is the value of (2#3) & (7#0)?

**B4. **(see #9 above.) Suppose we do not insist on an *integer* in #9 above. How (if any) does that change the answer?

1. Homer.

2. The ball is thrown up.

3. 1 brick is 6 pounds, 1 1/2 bricks are 9 pounds

3+1/2x = x

3 = 1/2 ×

6 = x

4. 3, 5, 7

5. 48 = 15+16+17

27 = 8+9+10

6. Larry, I am an old fart and have no idea what is even being asked let alone know how to solve this one.

B2. 1,3,5 are not 3 consecutive prime numbers because mathematicians have a thing about the number 1.

Mathematicians make up excuses why 1 is excluded from the prime numbers, like 1 does not meet the definition of s prime. A prime number, according to mathematicians is an integer greater than one whose factors are itself and 1. So, mathematicians simply exclude 1 by definition. Is this fair? Mathematicians try to justify the definitiom excluding 1 by introducing the property of irreducibility and labeling 1 a unit rather than a prime. Poor number 1 being left out in the cold and bearing the weight of unity. I am reminded of the Three Dog Night song, One is the Lonliest Number.

Historically 1 was a prime and it has been a rather recent campaign started by Euclud to exclude 1 from the prime numbers.

There will be a march in Washington, D.C. in January with the hope President Trump will sign an axecutive order returning 1 to the ranks of primes.

1. Homer

2. He threw it straight UP

4. 3, 5, 7

5. sum of last 3 = 60

6. 33

1. WINTER

2. HE TOSSED IT STRAIGHT UP

3. 6.75

8.5

1.Homer

2.he threw it up in air

3. 9 lb

4. 3,5,7

5. 60

6.zero

7. $5.00

8. 5 children

9.54

10.

13. 2 quarters and a nickel ( one IS a nickel but one , at least, is not a nickel.

14. 14 days ( before the night comes and he slides back 3)

15.. His son

1. Homer

2. He threw the ball straight up in the air.

7. 5.00

8. 5 children

13. A half dollar and a nickel. The other coin is a nickel.

14. 14 Days

15. Himself

#10. 85

I didn’t try #10 before.

7. $5 in dimes

8. 5 children

9. 54

10. 85

B4. You could simply take the square root of 3000 and then give the decimal value ONE LESS than the specified decimal place (or choose a place to go to).

11. 72%

12. Zero