An Alternative To The Quiz Questions.

[Kimmy]

Sparkle = 4p
Wibbler = 23p
Nobbler = 13p

[Kimmy]

Fancy a day on the farm?




Puzzle 74

Farmer Stone is quite an eccentric dairy farmer. He originally had a total 54 gallons of milk in three churns and he wanted to make sure each churn contained 18 gallons of milk. In order to do this, he did the following:

First he poured 1/4 of the first churn in the second churn.
He then poured 1/2 of the second churn into the third churn.
Finally he poured 1/3 of the third churn into the first churn.

How many gallons did each churn contain before Farmer Stone started pouring?

[BC]

Feb 5, 2010 9:06:22 GMT Kimmy said:

Fancy a day on the farm?




Puzzle 74

Farmer Stone is quite an eccentric dairy farmer. He originally had a total 54 gallons of milk in three churns and he wanted to make sure each churn contained 18 gallons of milk. In order to do this, he did the following:

First he poured 1/4 of the first churn in the second churn.
He then poured 1/2 of the second churn into the third churn.
Finally he poured 1/3 of the third churn into the first churn.

How many gallons did each churn contain before Farmer Stone started pouring?

Working backwards...

"Finally he poured 1/3 of the third churn into the first churn"
Left 18 - 18 - 18

so it must have been 9 - 18 - 27

"He then poured 1/2 of the second churn into the third churn"
Left 9 - 18 - 27

so it must have been 9 - 36 - 9

"First he poured 1/4 of the first churn in the second churn"
Left 9 - 36 - 9

so it must have been 12 - 33 - 9

1st contained: 12
2nd contained: 33
3rd contained: 9

BC

[liz]

[Kimmy]

12, 33 and 9 gallons respectively for churns 1, 2 and 3. The solution may require more than one read!


Before After Therefore
>> Pour 1 C1 = 12 C1 = 9 C2 = +3
>> Pour 1 C2 = 33 C2 = 36
>> Pour 2 C2 = 36 C2 = 18 C3 = +18
>> Pour 3 C3 = 27 C3 = 18 C1 = +9
>> Pour 3 C1 = 9 C1 = 18

To explain a little further. After pour 3, C3 must have contained 18 gallons, so it must have contained 27 before the pour. Similarly after pour 2, C2 must have contained 18 gallons, so must have contained 36 before the pour. After pour 3, C1 must have contained 18 gallons, and it received 9 gallons from pour 3, so must have had 9 before the pour. So pour 1 left 9 gallons in C1, which means C1 contained 12 before the pour and C2 received 3 gallons. We know that C2 had 36 gallons before pour 2, so must have started with 33 gallons.

[Kimmy]

How are you getting on with these? Easy? Hard?

Its Saturday so lets do the football pools.





Puzzle 75

In a football syndicate, the winnings amounted to £7657. There were more than 30 people in the syndicate but less than 100. Each won exactly the same number of pounds and no pence were involved. How much did each win?

[BC]

Feb 6, 2010 11:43:12 GMT Kimmy said:

How are you getting on with these? Easy? Hard?

Its Saturday so lets do the football pools.





Puzzle 75

In a football syndicate, the winnings amounted to £7657. There were more than 30 people in the syndicate but less than 100. Each won exactly the same number of pounds and no pence were involved. How much did each win?

I thought to myself, it's always at the end. Save yourself some time and work down.

Blinking typical !! 31 people won £247 each.

BC

[Kimmy]

31 people: each won £247.

[Kimmy]

All you people looking in how are you getting on with these?

Come on post your answer.

Shy?

Don't be. Its just between you and me. Nobody else will know.


So you wont talk hey?

Sorry had to do it. I gave you a chance.


Anybody left out there have a go at this one and post your answer OR



Puzzle 77

Find a number whose double exceeds its half by exactly 99.

[liz]

77. 66 (Double 132. Half 33. Difference 99.)

[BC]

I agree Liz:

(2x) - (0.5*x) = 99
(132) - (33) = 99

so x = 66

[Kimmy]

66.

[Kimmy]

Its 'times' to post another one.

If you are not going to try and solve it and post your answer please do not read it.

I am watching you.

If I see you reading this and not posting your answer I will ;D

Puzzle 78

This multiplication contains the numbers 1-9. Can you complete it?

***
3* x
----
****

(The number 3 should be under the middle *.)

[BC]

Feb 8, 2010 8:58:25 GMT Kimmy said:

Its 'times' to post another one.

If you are not going to try and solve it and post your answer please do not read it.

I am watching you.

If I see you reading this and not posting your answer I will ;D

Puzzle 78

This multiplication contains the numbers 1-9. Can you complete it?

***
3* x
----
****

(The number 3 should be under the middle *.)

I have managed to work out what is required, and will set it out in a table:

	?	?	?
x		3	?
---	---	---	---
?	?	?	?

I'm not sure that's any clearer actually !!

Anyway, as for getting the answer... at the moment, I wouldn't know where to start, other than perhaps some laborious spreadsheet calculations !!

Good luck with this one Liz !!

BC

[Kimmy]

***
? 3* x
----
****

Due to the fact it will not copy and paste properly I will insert ? where there should be a gap.

[liz]

Spent a little time on this but no result, so far BC.

[BC]

I've spent too much time on it too Liz - even roped in Mrs BC whilst I went to the gym !!

I give in!!

[Kimmy]

186 x 39 = 7254.

[Kimmy]

How are you getting on with these during the long cold winter evenings?

Todays should warm you up.

We don't want any domestics trying to sort it out.


Puzzle 79

Can you find a five digit number that, if you place a 9 at the beginning to make a new number, is fours times larger than if you place the 9 at the end instead?

[BC]

Feb 9, 2010 9:06:16 GMT Kimmy said:

How are you getting on with these during the long cold winter evenings?

Todays should warm you up.

We don't want any domestics trying to sort it out.


Puzzle 79

Can you find a five digit number that, if you place a 9 at the beginning to make a new number, is fours times larger than if you place the 9 at the end instead?

The last number of the smaller is a 9, so I multiplied that by 4 to get the six at the end of the longer one. This made the lower number end 69. So I multiplied that by 4, which told me the last tow digits were 76.

At the top end, as the bigger number was going to start with a 9, the smaller one probably has to start with a 2.

I now knew the larger one was 92--76
and the smaller one was 2--769

From there, I got a little muddled, so went back to my tried and trusted "see if it works out" method! And finally, the number that worked out is...

23076

BC
Why does the room seem to be spinning?

[Kimmy]

23076: 923076 / 230769 = 4.

[Kimmy]

Are we having less nights over these questions? I do hope not.

I think I will pop down to the shop for some lemonade.


Puzzle 80

A local grocer delivers lemonade using two full 10 pint jugs. Recently, the grocer delivered to a pair of ladies who had a five pint jug and a four pint jug between them. Each wanted two pints of lemonade though. How did the grocer measure two pints into each jug only using the two 10 pint jugs and the ladies jugs? The jugs are not marked in any way and there was no other container which could be used.

[BC]

Feb 10, 2010 9:02:06 GMT Kimmy said:

Are we having less nights over these questions? I do hope not.

I think I will pop down to the shop for some lemonade.


Puzzle 80

A local grocer delivers lemonade using two full 10 pint jugs. Recently, the grocer delivered to a pair of ladies who had a five pint jug and a four pint jug between them. Each wanted two pints of lemonade though. How did the grocer measure two pints into each jug only using the two 10 pint jugs and the ladies jugs? The jugs are not marked in any way and there was no other container which could be used.

I've probably gone right aound the houses to get there, but I got there...

JUG SIZE	Start
- 10 -	10	5	5	5	9	9	10	10	10	10	10	10	10	6	6
- 10 -	10	10	6	10	10	6	6	7	7	3	3	8	8	8	10
- 05 -	0	5	5	1	1	1	1	0	3	3	5	0	2	2	2
- 04 -	0	0	4	4	0	4	3	3	0	4	2	2	0	4	2

The first column represents the jugs
The second column represents how they started off in terms of their contents.
The subsequent columns represent the pours from one jug into another.
Until finally, the 5L and 4L jugs contain 2 each.

Phew!

BC
Still spinning.

[liz]

BC - very well presented.

[BC]

Thanks Liz.

The thing is, it seems to me that these type of questions usually have a four or five step process, rather than the fourteen I've come up with! So the answer is probably much simpler.

Anyway, something to wile away the hours whilst I'm supposed to be working !!

BC

[Kimmy]

If we call the two 10 pint jugs jugA and jugB, the four pint jug4 and the five pint jug5 we can do the following.
Fill jug5 from jugA.
Fill jug4 from jug5.
Pour jug4 back into jugA.
Empty jug5 into jug 4.
Fill jug5 from jugA.
Fill jug4 from jug5.
Empty jug4 into jugA.
Fill jug4 from jugB.
Fill jugA from jug4.
Both jugs now contain 2 pints.

[Kimmy]

Looks like its time to get the Abacus out.

Come on let us know how you are getting on with these at home.

Are you finding them easy or hard?

If you are shy PM me the answer or better still post me the answer with a nice fat tip inside it.


Puzzle 81

Can you replace the question marks with maths symbols (+-/x) and make the equation correct:

(9 ? 1) ? (7 ? 6) ? (8 ? 4) = 3

[BC]

I fancy a take-away...

(9 - 1) - (7 - 6) - (8 - 4) = 3

which is

8 - 1 - 4 = 3

[Kimmy]

(9 - 1) - (7 - 6) - (8 - 4) = 3.

[Kimmy]

Can't stop talking today train to catch.




Puzzle 82

On my local railway track there is a tunnel which is 5 miles long. A train, which was 440 yards long, entered the tunnel at a speed of 50 miles per hour. How long did it take for the whole of the train to pass completely through the tunnel? [Note: there are 1760 yards in a mile].