An Alternative To The Quiz Questions.

[Kimmy]

Puzzle 27

Yesterday my mother asked me to buy some stamps. Stamps, in the land of BrainBashers, are available in 3p, 9p, 11p, 17p and 21p denominations. For three types of stamp I was asked to buy eight of each. For the other two types of stamp, I was asked to buy nine of each. Unfortunately I forgot which I was supposed to buy eight of and which to buy nine of. Luckily my mother had given me the exact money required to buy the stamps, £5.00 and the shopkeeper was able to give me the correct stamps. Which stamps did I buy?

[BC]

Dec 30, 2009 11:43:51 GMT Kimmy said:

Puzzle 27

Yesterday my mother asked me to buy some stamps. Stamps, in the land of BrainBashers, are available in 3p, 9p, 11p, 17p and 21p denominations. For three types of stamp I was asked to buy eight of each. For the other two types of stamp, I was asked to buy nine of each. Unfortunately I forgot which I was supposed to buy eight of and which to buy nine of. Luckily my mother had given me the exact money required to buy the stamps, £5.00 and the shopkeeper was able to give me the correct stamps. Which stamps did I buy?

Tricky.

I thought there were going to be hundreds of combinations, but in the end it came down to just 10. So I put them in a table:

Three of					Two of
3p	9p	11p	17p	21p	3p	9p	11p	17p	21p
0.24	0.72	0.88						1.53	1.89	5.26
0.24	0.72		1.36				0.99		1.89	5.20
0.24	0.72			1.68			0.99	1.53		5.16
0.24		0.88	1.36			0.81			1.89	5.18
0.24		0.88		1.68			0.99		1.89	5.68
0.24			1.36	1.68		0.81	0.99			5.08
		0.88	1.36	1.68	0.27	0.81				5.00
	0.72		1.36	1.68	0.27		0.99			5.02
	0.72	0.88		1.68	0.27			1.53		5.08
	0.72	0.88	1.36		0.27				1.89	5.12

Which shows there are:

8 x 11p = 0.88
8 x 17p = 1.36
8 x 21p = 1.68
9 x 3p = 0.27
9 x 9p = 0.81

Totals £5.00

[Kimmy]

Eight lots of 11p, 17p and 21p and nine lots of 3p and 9p. The shopkeeper rightly figured that I required eight lots of each of the stamps, which came to £4.88, he also knew I required two more stamps which added up to the difference.

[Kimmy]

Puzzle 26

What four digit number has digit 1 three less than digit 4 which is one more than digit 2 which is twice digit 3 which is not a prime number and is one more than 1/3 of digit 4?

[BC]

6849 ?

[Kimmy]

6849.

[Kimmy]

Puzzle 27

My brother, Julian, is a little simple. I recently asked him to buy me some ribbon for my daughter's pretty pink bonnet. He went to the haberdashery shop for the required length but accidentally interchanged the feet and inches. When I measured the resulting ribbon I only had 30% of the length I required. How much ribbon did I originally ask for?

[BC]

Jan 1, 2010 10:03:28 GMT Kimmy said:

Puzzle 27

My brother, Julian, is a little simple. I recently asked him to buy me some ribbon for my daughter's pretty pink bonnet. He went to the haberdashery shop for the required length but accidentally interchanged the feet and inches. When I measured the resulting ribbon I only had 30% of the length I required. How much ribbon did I originally ask for?

9 feet 2 inches

9' is 108" + 2" = 110"

2' is 24" + 9" = 33"

30% of 110" = 33".

And to think I tried to work it out using that complicated equasion stuff you gave before. Doh!

[Kimmy]

I asked for 9 foot 2 inches (110 inches) and my brother brought me 2 foot 9 inches (33 inches).

[Kimmy]

Puzzle 28

Sally likes soda very much. At the local convenience store, for 5 empty soda bottles she receives a full bottle. As part of the Girl Guide's recycling initiative, she manages to collect 77 empty bottles. How many bottles of soda will she be able to drink in total?

[Kimmy]

Hope you are trying these at home. I have got them all correct so far. Having the answers of course.

[BC]

Jan 2, 2010 10:04:57 GMT Kimmy said:

Puzzle 28

Sally likes soda very much. At the local convenience store, for 5 empty soda bottles she receives a full bottle. As part of the Girl Guide's recycling initiative, she manages to collect 77 empty bottles. How many bottles of soda will she be able to drink in total?

She gets 15 sodas (15 x 5 = 75) with two empties remaining.

She gets 3 sodas when she's drunk the 15.

She gets 1 soda when she's drunk the 3, using the 2 that remained before.

15 + 3 + 1

So, she will be able to drink 19 sodas, assuming she doesn't explode first.

BC

[Kimmy]

19 bottles: from the initial 77 bottles, she receives 15 full bottles (with 2 spare empties). From the 17 empties, she receives 3 more full bottles (with 2 spare empties). From the 5 empties she receives one final full bottle.

[Kimmy]

Puzzle 32

During a recent expedition, three intrepid adventurers were left stranded in the middle of the desert with only a crate full of apples. During the night, Alan woke up and decided to hide his share of the apples and hid a third, then promptly fell asleep again. Brian woke up shortly after and also decided to hide a third of the remaining apples and he also dozed back to sleep. Finally, Charlie woke up and seeing the others were asleep, took a third of what was left. Of course none of the adventurers knew of the other's antics, so, in the morning, they shared the remaining apples, each receiving sixteen. How many apples were in the crate originally?

[Kimmy]

How are you getting on with these at home?
Come on don't be

[liz]

32. 162

[BC]

Jan 3, 2010 12:41:46 GMT liz said:

32. 162

I'll go along with that.

Good to have another player here Liz.

[Kimmy]

162: Alan hid 54, leaving 108. Brain hid 36, leaving 72. Charlie hid 24, leaving 48. 48 apples were then available to share in the morning.

[Kimmy]

Puzzle 34

How many days before 17th August is it, if 50 days ago, it was four times as many days since March 30th?

[liz]

34. 18 days

[BC]

I was struggling with that one. Well done Liz.

[Kimmy]

18 days: 30th July. 17 August - 18 days = 30 July. 30 July - 50 days = 10 June. 10 June - 30 March = 72 days, which equals 4 x 18.

[Kimmy]

Puzzle 35

There is a number.

1. If it is not a multiple of 4, then it is between 60 and 69.
2. If it is a multiple of 3 it is between 50 and 59.
3. If it is not a multiple of 6 it is between 70 and 79.

What is the number?

[BC]

Jan 5, 2010 10:21:32 GMT Kimmy said:

Puzzle 35

There is a number.

1. If it is not a multiple of 4, then it is between 60 and 69.
2. If it is a multiple of 3 it is between 50 and 59.
3. If it is not a multiple of 6 it is between 70 and 79.

What is the number?

I had mucho head scratchi over this one.

But here is it 76

76 is a multiple of 4,so is not between 60 and 69.
76 is not a multiple of 3 so is not between 50 and 59.
76 it is not a multiple of 6 so is between 70 and 79.

[Kimmy]

76. Where do we start to find the answer?! Let's try a random guess: is it 10? No. Why? As 10 isn't a multiple of 4 it would have to be between 60 and 69 (by #1). Therefore, if it isn't a multiple of 4, it must lie between 60 and 69 (and not be a multiple of 4), i.e. 61, 62, 63, 65, 66, 67 or 69. It can't be a multiple of 3 (by #2) therefore only 61, 62, 65, 67 remain. However, by #3 none of these numbers is allowed (as none is a multiple of 6). Therefore we've reached a contradiction, and the number MUST be a multiple of 4. Let's try another random number now, 8 say, but by #3 the number must be between 70 and 79, so another contradiction. So, either the number is a multiple of 6, or between 70 and 79 (and not a multiple of 6). Every multiple of 6 is also a multiple of 3, therefore by #2 we're looking for a number between 50 and 59, which is a multiple of 3, i.e. 51, 54, 57, BUT by #1 none of these is allowed. Therefore by #3, the number lies between 70 and 79. We know it's a multiple of 4 (by #1) which leaves only 72 and 76, but by #2 (and #3) we can rule out 72. Which only leaves 76!

[Kimmy]

Puzzle 36

If you were to spell out the numbers in full, (One, Two, Three, etc), how far would you have to go until you found the letter 'A'?

[BC]

[liz]

36. 1,000

[Kimmy]

1000: one thousand. Unless you in the UK when 101 = one hundred And one.

[Kimmy]

Puzzle 37

Take the number of days in a leap year, add the number of months with 30 days, divide by the number of loafs in a baker's dozen, add the number of days in March, add the square root of nine, divide by the number of days in a week. Which month are you left with?