An Alternative To The Quiz Questions.

[liz]

155. 7 chickens.

280 ants = 1680 feet
28 mice = 112 feet
7 chickens = 14 feet

Total 1806 feet

[Kimmy]

There are 7 chickens, 28 mice and 280 ants. For every chicken (2 legs) we have 4 mice (16 legs) and 40 ants (240 legs) = 258 legs. So we can divide the total number of legs by 258, giving 1806 / 258 = 7 (chickens).

[Kimmy]

Puzzle 156

Can you find a number such that its double is fourteen more than its quarter?

[Kevin THFC]

8

2 x 8 =16
0.25 x 8 =2

16-2 =14

[BC]

I see I shall have to get in here earlier!

I agree. 8 it is.

[liz]

I agree as well.

[Kimmy]

8.

[Kimmy]

Puzzle 157

My current age, is the age of my brother (who is 14), plus one third of my age. How old will I be when my brother is twice his current age?

[Kevin THFC]

35

[BC]

Apr 20, 2010 15:50:13 GMT Kimmy said:

Puzzle 157

My current age, is the age of my brother (who is 14), plus one third of my age. How old will I be when my brother is twice his current age?

I agree again. I'll give the workings this time!

A = 14 x ( A / 3 )

A must be a multiple of 3, and the multiple that fits is 21. So in 14 years, you'll be 35. (You wish ;D )

[Kimmy]

I will be 35 (in 14 years time): I am currently 21.

If x is my current age, then:

x = 14 + x
-
3
so

3x = 42 + x

and

2x = 42

So

x = 21
I am currently 21 and my brother is currently 14, when he is 28 (double his age) I will be 35.

[Kimmy]

Puzzle 160

At the annual puzzle discussion conference, 20 people attended. At the start of the conference, each person shook hands with every other person, how many handshakes took place in total?

[Kevin THFC]

190

[BC]

Apr 21, 2010 17:48:43 GMT Kimmy said:

Puzzle 160

At the annual puzzle discussion conference, 20 people attended. At the start of the conference, each person shook hands with every other person, how many handshakes took place in total?

19 + 18 + 17 + 16 + 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = ...I agree again... 190.

Must get here earlier. Bloomin' Spurs supporters. They get everywhere. (My dad was one god bless him). Funnily enough, I went to a family party on Saturday night (Mrs. BC's family that is) and it was amazing how many of them made a point of coming over to say 'hello' to me. Yes, they were all Spurs supporters too. I've never been so popular with Mrs. BC's family before. ;D

BC

[Kimmy]

190: the first person shook hands with 19 others, the second had already shook hands with the first and therefore shook 18 hands, etc: 19+18+17+16+15+14+13+12+11+10+9+8+7+6+5+4+3+2+1 = 190.

[Kimmy]

Puzzle 162

I have three children. The youngest is the same age as the first digit in my age, another is the same age as the second digit in my age, and the third is the same age as the sum of the two digits in my age. None of the children are the same age and the total of our ages is 33. How old am I?

[BC]

Apr 22, 2010 18:01:38 GMT Kimmy said:

Puzzle 162

I have three children. The youngest is the same age as the first digit in my age, another is the same age as the second digit in my age, and the third is the same age as the sum of the two digits in my age. None of the children are the same age and the total of our ages is 33. How old am I?

23

Child 1 = x+y
Child 2 = y
Child 3 = x

My age = xy

x + y + (x+y) + xy = 33

2 + 3 + 5 + 23 = 33

BC

[Kimmy]

23, the children are 2, 3 and 5.

[Kimmy]

Puzzle 163

The BrainBashers mechanical computer is a very sensitive device, in consists of four sequential cog wheels which are in constant mesh. The largest cog has 63 teeth and the others have 42, 35 and 27 respectively. By accident, Daniel started to rotate the largest cog. How many revolutions must he rotate the largest cog make before the computer is back in its starting position with all of the cogs where they started?

[BC]

Twice.

63,42,35,27
Revolve them once, and the positions are:
63,21,28,36 (deduct the smaller figures from 63)
Revolve them again:
63,42,35,27

I think that's how you do it anyway.

BC

[Kimmy]

30 revolutions. If we break each wheel into its prime factors, we get:

63 = 3 x 3 x 7
42 = 2 x 3 x 7
35 = 5 x 7
27 = 3 x 3 x 3

We now think of rotating the large wheel just once, and this is 3 x 3 x 7 teeth moved (3 x 21), and we can see that 42 tooth wheel also has a 3 x 7 (21 teeth) in it, with an extra 2. If we therefore rotate the 63 toothed wheel twice, the 42 will have rotated three times.

The answer involves cancelling any common factors from the large wheel. We can cancel 3, 3, 7 from any of the smaller ones to leave 2 (from the 42), 5 (from the 35) and 3 (from the 27). 2 x 5 x 3 = 30.

[Kimmy]

The legendary Kimmypops calendar has had a small problem. Here is a listing showing the number of days in each month:

January 73
February 83
March 51
April 52
May 31
June 42
July 41
August 63
September ==?==

Using the same rules, how many days are in September?

[BC]

93

Consonant = 10
Vowel = 11

BC

[Kimmy]

The ink was still wet. ;D

93: the first digit is how many letters there are in the word, the second digit is how many vowels there are.

[Kimmy]

Puzzle 165

My Kimmypops electronic world atlas has developed a fault, I did a listing of miles from England to particular countries and here is the result:

America 1,800 miles
New Zealand 2,400 miles
Japan 1,200 miles
Brazil 1,400 miles

How far away did it list Argentina as?

[BC]

2200.

Consonant = 200
Vowel = 300

[liz]

[Kimmy]

2,200 miles: vowels are worth 300 miles and consonants are worth 200 miles.

[Kimmy]

Puzzle 166

Last week, I travelled from London to Stoke. On the first day I travelled one half of the distance. On day two, I travelled one third of the remaining distance. On day three, I travelled three quarters of the remaining distance. Yesterday I travelled one half of the remaining distance. I now have 5 miles left to travel. How far is it from Stoke to London in total?

[Kevin THFC]

120 miles