Riddles and Puzzles

[classic33]

Website Interest
My friend's music fan website started out fast: lots of visitors the first week. But every week, there were fewer and fewer; the second week there was one more visitor than 2/3 of the first week, the 3rd week there were 2 more than 2/3 of the second week, the 4th week there were 3 more than 2/3 of the 3rd week, and so on, until the final week, when there were just 533.

How many weeks was the website up?
How many visitors did it get the 1st week?
How many total visitors were there?

 

[AndyRM]

I think I've got the ant one, I've no clue about the buckets though the question reminds me of a Crystal Maze challenge. Website I will have a think about!

 

[shouldbeinbed]

the buckets one is a trick question isn't it.

 

[Nihal]

No matter...whether Ascending or Descending order
We have 4 buckets( A,B,C, and D)
(A) can take only 3 gallons of water,
(B) can take 4 gallons...they are both empty at start position.
(C) and (D) have the same size, each can take exactly 5 gallons, both are full with water to start with.

Use these beakers only to make an ascending or descending order of water amount in each beaker...
i.e. , either...1 gallon, 2,3,and 4 gallons,
or 4 gallons, 3,2 and one gallon...
Have a nice time..

That's easy

Pour D into B,leaves you with 1 gallon in D and four in B
Pour C into A which leaves 3 in A and 2 in C

DCAB or BACD.


Do we have to get them alphabetical order?ABCD or DCBA or will any order do?

 

[nickyboy]

That's easy

Pour D into B,leaves you with 1 gallon in D and four in B
Pour C into A which leaves 3 in A and 2 in C

DCAB or BACD.


Do we have to get them alphabetical order?ABCD or DCBA or will any order do?

I fear they have to be in alphabetical order, which is an all together more complicated problem! After messing about with about 20 iterations of pouring from one to another last night I gave up. The only tip I can give (and please take with a pinch of salt) is that it must be A=1, B=2, C=3, D=4 as A will not hold 4 gallons.

Might have another go later today

 

[benb]

Website Interest
My friend's music fan website started out fast: lots of visitors the first week. But every week, there were fewer and fewer; the second week there was one more visitor than 2/3 of the first week, the 3rd week there were 2 more than 2/3 of the second week, the 4th week there were 3 more than 2/3 of the 3rd week, and so on, until the final week, when there were just 533.

How many weeks was the website up?
How many visitors did it get the 1st week?
How many total visitors were there?

10 weeks. 1st week was 19677. Or:
2 weeks. 1st week was 798 (but at least 3 weeks was implied in the question)

I can't help thinking there must be more solutions, but I've gone up to 100 weeks with no other solutions.

 

[machew]

Time Travelling Ant
It is 6 o'clock ..the ant from the tip of the clock's half foot Hour-hand must travel home to12 o'clock mark under the tip of 1ft Second-hand.
The clocks Minute hand is 9 inches.

The ant travels 1ft/min along the hands without stopping and reverses its direction when reaching the pivot end or the tip of the hands .
It can shift to any hand that is directly above or below it while resuming direction.

How long shall it take for the ant to arrive home?

3 minutes. Ant walks 6 inches to the base of the hour hand and switches to the second hand when it has the chance. He will have switched direction moving up the second hand, but can switch to the minute hand when the second hand overlaps it (approx 6 inches up it). He then walks up and back down the minute hand switching back onto the second hand as he is turning around to move back up the minute hand. After walking to the tip of the second hand he will have traveled 36 inches exactly meaning he is at the 12 and reached his home.

 

[machew]

Use three 9's and arrange them using the mathematical signs to form the number one.

 

[nickyboy]

Use three 9's and arrange them using the mathematical signs to form the number one.

9 x 9 / 9squared

 

[nickyboy]

You have 8 eggs. One egg has gone off and is heavier than the others. You have a set of balancing scales. What is the minimum number of times you need to use the scales to identify the heavier egg?

 

[benb]

You have 8 eggs. One egg has gone off and is heavier than the others. You have a set of balancing scales. What is the minimum number of times you need to use the scales to identify the heavier egg?

I can't get lower than 3.

 

[nickyboy]

I can't get lower than 3.

Good effort but three is not the minimum

 

[Nihal]

7

If all weigh the same,the last one.

 

[Archie_tect]

2 weighings...

 

[benb]

Good effort but three is not the minimum

Ooh, I've worked out how to do it in 2.

Number the eggs. Split into two groups of 3 and one of 2.
Weigh the groups of 3 against each other. If the scales level, then the heavier egg must be in the group of 2, so weigh those eggs against each other.

If they don't balance, take the heavier of the group of 3, and weigh 2 of the eggs from that group against each other, keeping the 3rd egg to one side.
If the scales don't balance, you've discovered the heavier egg. Otherwise the egg you put to to one side is heavier.