An Alternative To The Quiz Questions.

[Kimmy]

Right everybody. Get your calculators out:

Puzzle 62

The BrainBashers calculator is low on batteries again. The following multiplication is wrong. Each line has the correct numbers, but mixed up. The solution is correct though.

2147
3725 *
========
22084429

[liz]

Puzzle 62

4217 x 5237 = 22,084,429

[Kimmy]

4217 * 5237 = 22084429.

[Kimmy]

Ready? Here we go.




Puzzle 63

Can you find an eight digit number with the following property. The first digit tells you how many zeros there are in the number, the second digits tells you how many ones there are in the number, the third digit tells you how many twos there are in the number, etc. For example, with the number 21200, there are 2 zeros, 1 one, 2 twos, 0 threes and 0 fours. What is the required eight digit number?

[BC]

How about :

42101000

There are:

4 x 0
2 x 1
1 x 2
0 x 3
1 x 4
0 x 5,6,7

BC

[Kimmy]

42101000.

Did you get it?

[Kimmy]

Were you at the gala? Perhaps you counted the children.

Puzzle 64

At a local village gala, the entire population turned up, 500 people. The event raised £3,000. Tickets were priced as follows:

£7.48 men
£7.12 women
£0.45 children.

How many children were there?

[BC]

Jan 29, 2010 11:04:03 GMT Kimmy said:

Were you at the gala? Perhaps you counted the children.

Puzzle 64

At a local village gala, the entire population turned up, 500 people. The event raised £3,000. Tickets were priced as follows:

£7.48 men
£7.12 women
£0.45 children.

How many children were there?

I think there were 200 kiddiewinks there.

200 chilblains @ 45p = £90

1 mammas + 1 pappa = £15.

So if there were 194 couples there @ £15 = £2,910.

£2910 + £90 = £3,000.

I do like doing these.

BC

[BC]

By the way... who prices tickets using odd pence?

And another thing, why are men being unfairly discriminated against - having to pay a higher entrance fee. Outrageous!

[Kimmy]

92: with 149 men and 259 women. The best way is to fix the number of children and play around with the numbers of the men and women to see what happens as these are changed. It soon becomes apparent how changing the children changes the answer and 92 is soon found.

[Kimmy]

Puzzle 65

Yesterday I went for a long bicycle ride around the local lakes. As the ride was quite long, I rode in various stages. In the first stage I rode half of the overall distance. Stage two saw half of the remaining distance plus 35 metres covered. Stage three covered three-quarters of the remaining distance. Stage four completed half of the remaining distance plus 75 metres. Stage five completed the journey with a final burst of 150 metres. How far did I cycle in total?

[BC]

Jan 30, 2010 20:37:17 GMT Kimmy said:

Puzzle 65
Yesterday I went for a long bicycle ride around the local lakes. As the ride was quite long, I rode in various stages. In the first stage I rode half of the overall distance. Stage two saw half of the remaining distance plus 35 metres covered. Stage three covered three-quarters of the remaining distance. Stage four completed half of the remaining distance plus 75 metres. Stage five completed the journey with a final burst of 150 metres. How far did I cycle in total?

Have to work backwards on these methinks...

Stage 5 = 150*

Stage 4
150 + 75 + 225 = 450*

Stage 3
600 is left, so x4 = 2400*

Stage 2
2400 + 35 + 2435 = 4870*

Stage 1
150 + 450 + 2400 + 4870 = 7870*

Total distance is 2 x 7870 = 15,740

BC

---

Yesterday's: I can't add up! 7.12 + 7.48 is 14.50, not 15. What are they teaching kids these days eh? Ahem.

[Kimmy]

7340 metres.

Stage 1: cycled 3670 leaving 3670
Stage 2: cycled 1870 leaving 1800
Stage 3: cycled 1350 leaving 450
Stage 4: cycled 300 leaving 150
Stage 5: cycled 150 leaving 0

[Kimmy]

How are you getting on at home?

Don't be shy you can tell me.

Nobody else will know only you and me.

So you wont talk hey?

Fasten your seat belts for this one.



Puzzle 67

A plane maintains an average speed of 696mph from London to New York. It then returns from New York to London at an average speed of 145mph. What is the average speed for the entire journey?

[BC]

Jan 31, 2010 12:39:32 GMT Kimmy said:

7340 metres.

Stage 1: cycled 3670 leaving 3670
Stage 2: cycled 1870 leaving 1800
Stage 3: cycled 1350 leaving 450
Stage 4: cycled 300 leaving 150
Stage 5: cycled 150 leaving 0

I went wrong at stage three. There was no need for me to add the 150 back onto the 450. Foiled again.

[BC]

Jan 31, 2010 12:43:46 GMT Kimmy said:

Puzzle 67
A plane maintains an average speed of 696mph from London to New York. It then returns from New York to London at an average speed of 145mph. What is the average speed for the entire journey?

240mph

If the one-way distance was 1000 miles (for example), the outward journey took 1000/696 hours and the return journey took 1000/145 hours. Therefore the total time taken was (1000/696 + 1000/145) hours for 2000 miles. So the average speed was 2000 / (1000/696 + 1000/145) which equals 240mph. The answer remains the same if you change the distance to any number of miles.

BC

---

I'm not clever. I just remembered where to find the formulae!

[Kimmy]

240mph: let the distance be x miles. Therefore, the outward trip takes x / 696 hours and the return trip takes x / 145 hours. The total distance travelled is hence 2x, in a time of (x / 696 + x / 145). Therefore the speed (distance / time) is given by 2x / (x / 696 + x / 145) = 240 mph.

[Kimmy]

Did you get the last one?

Will you get this one?



Puzzle 68

The area of the floor of the tank is 6 square feet, and the water in it is 9 inches deep. How much does the water rise if a 1-foot metal cube is placed in it? How much further does the water rise if a second 1-foot cube is also placed in the tank?

[BC]

Feb 1, 2010 12:59:53 GMT Kimmy said:

Did you get the last one?

Yes.

Feb 1, 2010 12:59:53 GMT Kimmy said:

Will you get this one?

No, I don't think so.

Feb 1, 2010 12:59:53 GMT Kimmy said:

Puzzle 68

The area of the floor of the tank is 6 square feet, and the water in it is 9 inches deep. How much does the water rise if a 1-foot metal cube is placed in it? How much further does the water rise if a second 1-foot cube is also placed in the tank?

My brain hurts.

Part 1

If there had been 12" of water, the first cube would have raised the level by 1/2".

But as there is only 9" of water, I am getting in a proper muddle.

I think perhaps there is 9/12ths (or 3/4) of 1/2". Which is 3/8ths of an inch.

---

Part 2

If you introduce a second cube, it depends how you place it! If you stack it on top of the first cube, then it doesn't add to the water level !! But I suspect that's me looking for the easy way out.

Mmm... I may have a go at part 2 later. That looks tough.

[BC]

Part 2

Now my brain really hurts.

But just as I was about to quit, I think I got it.

Two blocks mean there are now 18 segments of 12"x24".

If the water started off at 12", it would mean a rise of 0.67".

But as there are only 9", 3/4 of 0.67" is just about 1/2 an inch.

Any good?

[Kimmy]

1.8 inches, then another 2.2 inches. Initially the volume of water is 6 * 9/12 = 4.5 cubic feet. The first cube effectively reduces the cross-sectional area of the tank to 5 square feet, causing the water to be 4.5/5 foot = 10.8 inches deep. Therefore rises 1.8 inches. The second cube is then placed on the floor of the tank, the cross-sectional area is 4 square feet up to a height of 1 foot, and this is filled by 4 cubic feet of water. The remaining 0.5 cubic foot, in a cross-sectional area of 6 square feet, requires a height of 0.5/6 foot = 1 inch. The water is therefore 13 inches deep and has risen by another 2.2 inches.

[Kimmy]

Back out on dry land but not for long now into the air.




Puzzle 69

The Winter Olympics are well underway and I am working out the plane times for the return journeys. Unfortunately, the timetable software is playing up again and has worked out the times incorrectly, as shown below.

Turkey 4.00pm
Mexico 3.00pm
Jamaica 5.00pm
Japan 1.00pm

According to the software, at what time is the return trip to Finland?


Please help everybody out there. I don't know where to start.

[Kimmy]

Well I got back. Did you work it out?



7.00pm. Each vowel of the word is worth 2 hours and each consonant is worth 3 hours. The time shown is the number of hours past midnight of the return trip.

[Kimmy]

Come on now I know you have all got £ notes and coins under the bed.




Puzzle 71

A numismatist decides to divide his coin collection between his children. The oldest gets 1/2 of the collection, the next gets 1/4, the next gets 1/5, and the youngest gets the remaining 49 coins. How many coins are in the collection?

[liz]

71.
490 - 1st child
245 - 2nd
196 - 3rd
49 - 4th

Total 980 coins

[BC]

Feb 3, 2010 11:33:00 GMT liz said:

71.
490 - 1st child
245 - 2nd
196 - 3rd
49 - 4th

Total 980 coins

I concur.

[Kimmy]

There are 980 coins in the collection: 490 + 245 + 196 + 49 = 980.

[Kimmy]

For those with a sweet tooth.


Puzzle 72

At the local sweet shop, three particularly nice sweets are on special offer. A Sparkle, a Wibbler and a Nobbler together cost 40p. A Nobbler is over three times the price of a Sparkle. Six Sparkles are worth more than a Wibbler. A Nobbler, plus two Sparkles costs less than a Wibbler. Can you determine the price of each type of sweet?

[michael]

don't know if it's right but i got
Nobbler = 13p
Wibbler = 23p
Sparkles = 4p

have fun

[BC]

That's what I get too.