OK. I think Bill is suffering from sleep deprivation.

4 weights of 1, 3, 9, and 27lb can be combined to give any single whole number of lb's between 1 and 40.

F.

Well done Fred! You got the correct answer... 1 point to you!
Q48 Answer 1: 1, 3, 9, 27 lb

Standings:
1. William Rothamel - 10 1/2 Points
2. Fred W - 7 1/2 Points
3. Mr. Kevvy - 7 Points
4. Guido.Man - 7 Points
5. Sarge - 5 1/2 Points
6. WinterKnight - 5 Points
7. Dominique - 4 1/2 Points
8. John McLeod VII - 1 Point
9. Labbie - 1 Point
10. Scary Capitalist - 1/2 Point
11. TBD...

There is another correct answer to Q48, It will be worth 1/2 a point, so the question will be kept open... for now I'm off to an early bed (10:30 PM NZST right now) so I'll see if anyone has anymore answers in my morning (6:30 AM NZST)


Q47: A shopkeeper wants to be able to dispense sugar in whole pounds ranging from one pound up to 40 pounds. He has a standard, equal-arm balance weigh scale. Being of an extremely economical outlook, he wants to use the least possible number of weights to enable him to weigh any number of pounds between 1 and 40. How many weights does he need and what are they? (Answer cannot be 1, 3, 9, and 27 lbs....)

Luke has signed off...

Best Regards to all.

---

- Luke.

Well done Fred! You got the correct answer... 1 point to you!
Q48 Answer 1: 1, 3, 9, 27 lb

These are all base 3. Well this would validate the theory that e at 2.718 is the most compact number base; and why when i worked on base three threshold logic, gate counts were minimized as compared to binary.

This is the answer if the requirement was to have a single weighing. For those of us who like to think outside the box and look at the problem from all sides we would have to scold Luke for another incompletely specified problem.

That's OK Luke we love you any way and I can't be a sore loser --good for you there Fred. I didn't see that you could easily put the weights on the other side of the balance to count up to each poundage. this suggests some new numbering schemes to me. Way to go !!

back to sleep now for sure.

Bill

Q47 Answer 2 is still open, but I'll give out 48 anyway....

Q47 : A shopkeeper wants to be able to dispense sugar in whole pounds ranging from one pound up to 40 pounds. He has a standard, equal-arm balance weigh scale. Being of an extremely economical outlook, he wants to use the least possible number of weights to enable him to weigh any number of pounds between 1 and 40. How many weights does he need and what are they? (Answer cannot be 1, 3, 9, and 27 lbs....)

Q48 : A man came to a river carrying a fox, a duck, and a bag of corn. There was a boat in which he could ferry of the three items across the river at any one time. He could not leave the fox alone with the duck, nor the duck alone with the corn, so how did he get all three across?

Best Regards,
Luke.

---

- Luke.

Q47 Answer 2 is still open, but I'll give out 48 anyway....

Q47 : A shopkeeper wants to be able to dispense sugar in whole pounds ranging from one pound up to 40 pounds. He has a standard, equal-arm balance weigh scale. Being of an extremely economical outlook, he wants to use the least possible number of weights to enable him to weigh any number of pounds between 1 and 40. How many weights does he need and what are they? (Answer cannot be 1, 3, 9, and 27 lbs....)

Q48 : A man came to a river carrying a fox, a duck, and a bag of corn. There was a boat in which he could ferry one / two(?) of the three items across the river at any one time. He could not leave the fox alone with the duck, nor the duck alone with the corn, so how did he get all three across?

Best Regards,
Luke.

Q48:I think you omitted one of the words I have inserted in bold (fairly important!).

F.

---

Q47 Answer 2 is still open, but I'll give out 48 anyway....

Q47 : A shopkeeper wants to be able to dispense sugar in whole pounds ranging from one pound up to 40 pounds. He has a standard, equal-arm balance weigh scale. Being of an extremely economical outlook, he wants to use the least possible number of weights to enable him to weigh any number of pounds between 1 and 40. How many weights does he need and what are they? (Answer cannot be 1, 3, 9, and 27 lbs....)

Q48 : A man came to a river carrying a fox, a duck, and a bag of corn. There was a boat in which he could ferry one / two(?) of the three items across the river at any one time. He could not leave the fox alone with the duck, nor the duck alone with the corn, so how did he get all three across?

Best Regards,
Luke.

Q48:I think you omitted one of the words I have inserted in bold (fairly important!).

F.

Ah! Thank you, Fred!

Here they are again for ya'!

Q47 : A shopkeeper wants to be able to dispense sugar in whole pounds ranging from one pound up to 40 pounds. He has a standard, equal-arm balance weigh scale. Being of an extremely economical outlook, he wants to use the least possible number of weights to enable him to weigh any number of pounds between 1 and 40. How many weights does he need and what are they? (Answer cannot be 1, 3, 9, and 27 lbs....)

Q48 : A man came to a river carrying a fox, a duck, and a bag of corn. There was a boat in which he could ferry one of the three items across the river at any one time. He could not leave the fox alone with the duck, nor the duck alone with the corn, so how did he get all three across? (I won't tell you what or why, but to get a easy answer from this question, you need to fiddle with the questions law and logic...)

Everyone have a go!

Best Regards,
Luke.

---

- Luke.

Q47 Answer 2 is still open, but I'll give out 48 anyway....

Q47 : A shopkeeper wants to be able to dispense sugar in whole pounds ranging from one pound up to 40 pounds. He has a standard, equal-arm balance weigh scale. Being of an extremely economical outlook, he wants to use the least possible number of weights to enable him to weigh any number of pounds between 1 and 40. How many weights does he need and what are they? (Answer cannot be 1, 3, 9, and 27 lbs....)

Q48 : A man came to a river carrying a fox, a duck, and a bag of corn. There was a boat in which he could ferry one / two(?) of the three items across the river at any one time. He could not leave the fox alone with the duck, nor the duck alone with the corn, so how did he get all three across?

Best Regards,
Luke.

Q48:I think you omitted one of the words I have inserted in bold (fairly important!).

F.

Ah! Thank you, Fred!

Here they are again for ya'!

Q47 : A shopkeeper wants to be able to dispense sugar in whole pounds ranging from one pound up to 40 pounds. He has a standard, equal-arm balance weigh scale. Being of an extremely economical outlook, he wants to use the least possible number of weights to enable him to weigh any number of pounds between 1 and 40. How many weights does he need and what are they? (Answer cannot be 1, 3, 9, and 27 lbs....)

Q48 : A man came to a river carrying a fox, a duck, and a bag of corn. There was a boat in which he could ferry one of the three items across the river at any one time. He could not leave the fox alone with the duck, nor the duck alone with the corn, so how did he get all three across? (I won't tell you what or why, but to get a easy answer from this question, you need to fiddle with the questions law and logic...)

Everyone have a go!

Best Regards,
Luke.

1. Transport duck and deposit on other side leaving fox and corn for later. Return alone.
2. Transport corn leaving fox alone. Deposit corn. Return with duck.
3. Leave duck where it started and transport fox. Deposit fox with corn. Return alone.
4. Transport duck (again).

F.

---

Well done! Fred, you are getting close to Bill!
Q48 Solved!

Standings!
1. William Rothamel - 10 1/2 Points
2. Fred W - 8 1/2 Points
3. Mr. Kevvy - 7 Points
4. Guido.Man - 7 Points
5. Sarge - 5 1/2 Points
6. WinterKnight - 5 Points
7. Dominique - 4 1/2 Points
8. John McLeod VII - 1 Point
9. Labbie - 1 Point
10. Scary Capitalist - 1/2 Point
11. TBD...

Got any answer to Q47 yet?

Q47 : A shopkeeper wants to be able to dispense sugar in whole pounds ranging from one pound up to 40 pounds. He has a standard, equal-arm balance weigh scale. Being of an extremely economical outlook, he wants to use the least possible number of weights to enable him to weigh any number of pounds between 1 and 40. How many weights does he need and what are they? (Answer cannot be 1, 3, 9, and 27 lbs....)

Q49 : Can you find the fifth term in the following series? 77, 49, 36, 18, ...

Best Regards,
Luke.

---

- Luke.

Well done! Fred, you are getting close to Bill!
Q48 Solved!

Standings!
1. William Rothamel - 10 1/2 Points
2. Fred W - 8 1/2 Points
3. Mr. Kevvy - 7 Points
4. Guido.Man - 7 Points
5. Sarge - 5 1/2 Points
6. WinterKnight - 5 Points
7. Dominique - 4 1/2 Points
8. John McLeod VII - 1 Point
9. Labbie - 1 Point
10. Scary Capitalist - 1/2 Point
11. TBD...

Got any answer to Q47 yet?

Q47 : A shopkeeper wants to be able to dispense sugar in whole pounds ranging from one pound up to 40 pounds. He has a standard, equal-arm balance weigh scale. Being of an extremely economical outlook, he wants to use the least possible number of weights to enable him to weigh any number of pounds between 1 and 40. How many weights does he need and what are they? (Answer cannot be 1, 3, 9, and 27 lbs....)

Q49 : Can you find the fifth term in the following series? 77, 49, 36, 18, ...

Best Regards,
Luke.

No further ideas on the Q47 yet :(
Q49: I can see a way of getting the next 2 terms to be 15 and 5 but it seems overly convoluted.

F.

---

Well done! Fred, you are getting close to Bill!
Q48 Solved!

Standings!
1. William Rothamel - 10 1/2 Points
2. Fred W - 8 1/2 Points
3. Mr. Kevvy - 7 Points
4. Guido.Man - 7 Points
5. Sarge - 5 1/2 Points
6. WinterKnight - 5 Points
7. Dominique - 4 1/2 Points
8. John McLeod VII - 1 Point
9. Labbie - 1 Point
10. Scary Capitalist - 1/2 Point
11. TBD...

Got any answer to Q47 yet?

Q47 : A shopkeeper wants to be able to dispense sugar in whole pounds ranging from one pound up to 40 pounds. He has a standard, equal-arm balance weigh scale. Being of an extremely economical outlook, he wants to use the least possible number of weights to enable him to weigh any number of pounds between 1 and 40. How many weights does he need and what are they? (Answer cannot be 1, 3, 9, and 27 lbs....)

Q49 : Can you find the fifth term in the following series? 77, 49, 36, 18, ...

Best Regards,
Luke.

No further ideas on the Q47 yet :(
Q49: I can see a way of getting the next 2 terms to be 15 and 5 but it seems overly convoluted.

F.

Some one will get Q47... Q49 is not 15 or 5 so I also can't give you the point yet.... please try again :)

Everyone else see my current questions above.

---

- Luke.

Well done! Fred, you are getting close to Bill!
Q48 Solved!

Standings!
1. William Rothamel - 10 1/2 Points
2. Fred W - 8 1/2 Points
3. Mr. Kevvy - 7 Points
4. Guido.Man - 7 Points
5. Sarge - 5 1/2 Points
6. WinterKnight - 5 Points
7. Dominique - 4 1/2 Points
8. John McLeod VII - 1 Point
9. Labbie - 1 Point
10. Scary Capitalist - 1/2 Point
11. TBD...

Got any answer to Q47 yet?

Q47 : A shopkeeper wants to be able to dispense sugar in whole pounds ranging from one pound up to 40 pounds. He has a standard, equal-arm balance weigh scale. Being of an extremely economical outlook, he wants to use the least possible number of weights to enable him to weigh any number of pounds between 1 and 40. How many weights does he need and what are they? (Answer cannot be 1, 3, 9, and 27 lbs....)

Q49 : Can you find the fifth term in the following series? 77, 49, 36, 18, ...

Best Regards,
Luke.

No further ideas on the Q47 yet :(
Q49: I can see a way of getting the next 2 terms to be 15 and 5 but it seems overly convoluted.

F.

Some one will get Q47... Q49 is not 15 or 5 so I also can't give you the point yet.... please try again :)

Everyone else see my current questions above.

Q49: I knew that it had to be simpler than my first thoughts!! 8 by multiplying the digits of each term to produce the next term in the series.

F.

---

Well done! Fred, you are getting close to Bill!
Q48 Solved!

Standings!
1. William Rothamel - 10 1/2 Points
2. Fred W - 8 1/2 Points
3. Mr. Kevvy - 7 Points
4. Guido.Man - 7 Points
5. Sarge - 5 1/2 Points
6. WinterKnight - 5 Points
7. Dominique - 4 1/2 Points
8. John McLeod VII - 1 Point
9. Labbie - 1 Point
10. Scary Capitalist - 1/2 Point
11. TBD...

Got any answer to Q47 yet?

Q47 : A shopkeeper wants to be able to dispense sugar in whole pounds ranging from one pound up to 40 pounds. He has a standard, equal-arm balance weigh scale. Being of an extremely economical outlook, he wants to use the least possible number of weights to enable him to weigh any number of pounds between 1 and 40. How many weights does he need and what are they? (Answer cannot be 1, 3, 9, and 27 lbs....)

Q49 : Can you find the fifth term in the following series? 77, 49, 36, 18, ...

Best Regards,
Luke.

No further ideas on the Q47 yet :(
Q49: I can see a way of getting the next 2 terms to be 15 and 5 but it seems overly convoluted.

F.

Some one will get Q47... Q49 is not 15 or 5 so I also can't give you the point yet.... please try again :)

Everyone else see my current questions above.

Q49: I knew that it had to be simpler than my first thoughts!! 8 by multiplying the digits of each term to produce the next term in the series.

F.

Correct answer! Fred!
Q49 Answer: 8

Standings:
1. William Rothamel - 10 1/2 Points
2. Fred W - 9 1/2 Points
3. Mr. Kevvy - 7 Points
4. Guido.Man - 7 Points
5. Sarge - 5 1/2 Points
6. WinterKnight - 5 Points
7. Dominique - 4 1/2 Points
8. John McLeod VII - 1 Point
9. Labbie - 1 Point
10. Scary Capitalist - 1/2 Point
11. TBD...

Fred, your just 1 point away from exacting Bill!

Q47 : A shopkeeper wants to be able to dispense sugar in whole pounds ranging from one pound up to 40 pounds. He has a standard, equal-arm balance weigh scale. Being of an extremely economical outlook, he wants to use the least possible number of weights to enable him to weigh any number of pounds between 1 and 40. How many weights does he need and what are they? (Answer cannot be 1, 3, 9, and 27 lbs....)

Q50 : Which is the smallest number which, when divided by 2, 3, 4, 5 and 6 will give 1, 2, 3, 4 and 5 as remainders, respectively?

Luke.

---

- Luke.

Well done! Fred, you are getting close to Bill!
Q48 Solved!

Standings!
1. William Rothamel - 10 1/2 Points
2. Fred W - 8 1/2 Points
3. Mr. Kevvy - 7 Points
4. Guido.Man - 7 Points
5. Sarge - 5 1/2 Points
6. WinterKnight - 5 Points
7. Dominique - 4 1/2 Points
8. John McLeod VII - 1 Point
9. Labbie - 1 Point
10. Scary Capitalist - 1/2 Point
11. TBD...

Got any answer to Q47 yet?

Q47 : A shopkeeper wants to be able to dispense sugar in whole pounds ranging from one pound up to 40 pounds. He has a standard, equal-arm balance weigh scale. Being of an extremely economical outlook, he wants to use the least possible number of weights to enable him to weigh any number of pounds between 1 and 40. How many weights does he need and what are they? (Answer cannot be 1, 3, 9, and 27 lbs....)

Q49 : Can you find the fifth term in the following series? 77, 49, 36, 18, ...

Best Regards,
Luke.

No further ideas on the Q47 yet :(
Q49: I can see a way of getting the next 2 terms to be 15 and 5 but it seems overly convoluted.

F.

Some one will get Q47... Q49 is not 15 or 5 so I also can't give you the point yet.... please try again :)

Everyone else see my current questions above.

Q49: I knew that it had to be simpler than my first thoughts!! 8 by multiplying the digits of each term to produce the next term in the series.

F.

Correct answer! Fred!
Q49 Answer: 8

Standings:
1. William Rothamel - 10 1/2 Points
2. Fred W - 9 1/2 Points
3. Mr. Kevvy - 7 Points
4. Guido.Man - 7 Points
5. Sarge - 5 1/2 Points
6. WinterKnight - 5 Points
7. Dominique - 4 1/2 Points
8. John McLeod VII - 1 Point
9. Labbie - 1 Point
10. Scary Capitalist - 1/2 Point
11. TBD...

Fred, your just 1 point away from exacting Bill!

Q47 : A shopkeeper wants to be able to dispense sugar in whole pounds ranging from one pound up to 40 pounds. He has a standard, equal-arm balance weigh scale. Being of an extremely economical outlook, he wants to use the least possible number of weights to enable him to weigh any number of pounds between 1 and 40. How many weights does he need and what are they? (Answer cannot be 1, 3, 9, and 27 lbs....)

Q50 : Which is the smallest number which, when divided by 2, 3, 4, 5 and 6 will give 1, 2, 3, 4 and 5 as remainders, respectively?

Luke.

Q50: 59
[Edit]
No complicated maths. Logic:

1: Remainder = 1 when divided by 2, therefore is odd.
2: Remainder = 2 when divided by 3, therefore 1 less than a multiple of 3.
3: Remainder = 4 when divided by 5, therefore ends in 4 or 9. But see 1 above - so ends in 9.
4: Since not directly divisible by 3, the sum of the digits preceding the 9 cannot be a multiple of 3.

Trial and error of numbers ending in 9, skipping 9 itself and 39, arrives pretty quickly at the answer of 59.
[/Edit]

---

Again, congratulations Fred + a special congratulations becuase you have tied with Bill as the top problem solver! Where is Bill?!
Q50 Answer: 59
Q50 Solver: Fred W

Standings:
1. William Rothamel - 10 1/2 Points
2. Fred W - 10 1/2 Points
3. Mr. Kevvy - 7 Points
4. Guido.Man - 7 Points
5. Sarge - 5 1/2 Points
6. WinterKnight - 5 Points
7. Dominique - 4 1/2 Points
8. John McLeod VII - 1 Point
9. Labbie - 1 Point
10. Scary Capitalist - 1/2 Point
11. TBD...

Q47 : A shopkeeper wants to be able to dispense sugar in whole pounds ranging from one pound up to 40 pounds. He has a standard, equal-arm balance weigh scale. Being of an extremely economical outlook, he wants to use the least possible number of weights to enable him to weigh any number of pounds between 1 and 40. How many weights does he need and what are they? (Apart from 1, 3, 9, and 27 lbs....)

Q51 : What is the letter where the question mark is: O T T F F S S E ? (this is a very nasty catch puzzle!)

Best Regards,
Luke.

---

- Luke.

ANSWER to Q51: N for nine

Just got up to get some water.

is it your birthday

Why not try my bean problem i want to see what fred and the others can do or if they like it.

Cheers,

Bill
AKA DADDIO

[quote]Again, congratulations Fred + a special congratulations becuase you have tied with Bill as the top problem solver! Where is Bill?!


Bill slept through the night --like a baby. sometimes I like to get up in the wee hours and check in with the rest of the world. I expect to be working again soon --in higher Education. so I may get to answer only the left overs from the thread since I will have to keep more regular hours then.

i would like to see more participation in your thread anyway so i am happy to let others have a go.

back to bed now.

best regards,

Bill

Well done Bill! You've regained your lead!

Question 51
Answer: N for Nine
Solver: Bill

Standings:
1. William Rothamel - 11 1/2 Points
2. Fred W - 10 1/2 Points
3. Mr. Kevvy - 7 Points
4. Guido.Man - 7 Points
5. Sarge - 5 1/2 Points
6. WinterKnight - 5 Points
7. Dominique - 4 1/2 Points
8. John McLeod VII - 1 Point
9. Labbie - 1 Point
10. Scary Capitalist - 1/2 Point
11. TBD...

Bill: You may post the bean problem in this thread anytime you like! I hope you still stick around even once your job, and lastly, without you and Fred, this thread would die, so I see not possibility of attracting new people...

No New Questions until my morning, but I'll leave everybody else with this old one:

Q47 : A shopkeeper wants to be able to dispense sugar in whole pounds ranging from one pound up to 40 pounds. He has a standard, equal-arm balance weigh scale. Being of an extremely economical outlook, he wants to use the least possible number of weights to enable him to weigh any number of pounds between 1 and 40. How many weights does he need and what are they? (Apart from 1, 3, 9, and 27 lbs....)

Best Regards,
Luke.

---

- Luke.

Ok
With Luke's permission, I am posting Q52 for youse guys (I used to live in New Jersey).

A math teacher passed out a sealed envelope to each of his students, telling them to keep it for later.

He then told them to put away their pencils and paper as well as their calculators.

Next, he posed the following Puzzle:

Mrs Murphy is going on a shopping spree--she buys a blouse that takes 1/4 of the money that she has in her purse. Next she buys a pair of shoes that take 1/3 of the remaining money in her purse. When she gets home (without making any other purchase) she finds that she has $38 dollars left in her purse.
How much money did she have in her purse to start with.

The teacher then said: Open your envelopes--there were four beans inside each one.

He then said" you must solve this problem using only the beans and your brain--no algebra or other scribblings "

What is the answer and how could the students solve the problem using the four beans?

Ok
With Luke's permission, I am posting Q52 for youse guys (I used to live in New Jersey).

A math teacher passed out a sealed envelope to each of his students, telling them to keep it for later.

He then told them to put away their pencils and paper as well as their calculators.

Next, he posed the following Puzzle:

Mrs Murphy is going on a shopping spree--she buys a blouse that takes 1/4 of the money that she has in her purse. Next she buys a pair of shoes that take 1/3 of the remaining money in her purse. When she gets home (without making any other purchase) she finds that she has $38 dollars left in her purse.
How much money did she have in her purse to start with.

The teacher then said: Open your envelopes--there were four beans inside each one.

He then said" you must solve this problem using only the beans and your brain--no algebra or other scribblings "

What is the answer and how could the students solve the problem using the four beans?

She started off with $76.

The 4 beans represented the total contents of the purse at the start.

The blouse cost 1 bean, leaving 3 beans.
The pair of shoes cost 1 bean, leaving 2 beans.
Therefore 2 beans = $38; i.e. 4 beans = $76

F.

---

fred is Right !

Luke will award you the point.

regards,

Bill.

Congratulations Fred! you answered Q52 correctly!

Standings:
1. William Rothamel - 11 1/2 Points
2. Fred W - 10 1/2 Points
3. Mr. Kevvy - 7 Points
4. Guido.Man - 7 Points
5. Sarge - 5 1/2 Points
6. WinterKnight - 5 Points
7. Dominique - 4 1/2 Points
8. John McLeod VII - 1 Point
9. Labbie - 1 Point
10. Scary Capitalist - 1/2 Point
11. TBD...

Q47 : Q47 : A shopkeeper wants to be able to dispense sugar in whole pounds ranging from one pound up to 40 pounds. He has a standard, equal-arm balance weigh scale. Being of an extremely economical outlook, he wants to use the least possible number of weights to enable him to weigh any number of pounds between 1 and 40. How many weights does he need and what are they? (Apart from 1, 3, 9, and 27 lbs....)

IMPORTANT!
I have been thinking about how to end this thread over the past month. I was also debating with myself to announce it here publicly, I have decided to let this thread run out to post 500, then if there is demand for it a Maths Problems II thread. But only if there is demand, which there is not right now.
What are your views???

---

- Luke.