The area of grass the goat can eat is 5,729.52 sq ft and is made up of three separate sections:
1. 3/4 of a circle produced by the goats 45 ft tether = 4,771.30 sq ft
2. 2 segments of a circle of radius 25 ft centred at nearest corners
= 866.66 sq ft
3. 2 triangles to complete the common area eaten from clockwise and anticlockwise grazing by the goat = 91.55 sq ft

The answer to this goat in a firld problem is 115.87 m and doesn’t require the radius of the feild to be used in the equation, since once the radio of the field radius and goat tethher is computes it’s a simple mater of multiplying by 100 – see proof at link to http://www.guggs.co.uk.

Are we sure the yellow box doesn’t already have a yellow star in it? What if the question were “How many boxes are missing their stars in this pattern?”? Would the answer be 2 or 3?

Only one jailer visit them to provide them with food. the first prisoner didn’t take his food at the fifth day which is the number of cities he sees from his cell. the second will notice that and sum both the cities he sees plus the 5 which corresponds to the number of evening it took for the other to hunger strike. since each look at half of the cities so the total number would be 10

I think there is a rule somewhere that says at least three cuts are needed to make seven pieces. Since the paper cannot be folded or bent so after the first cut the two pieces woujld be stacked for the second cut. I’m sure I could do it with actual paper but I’m having trouble seeing it in my head only.

L=length of rope
R=radius
As other answers have shown, this is a calculus problem. After reviewing many sites with this problem I have found an easy equation for deriving the area of the involute of the circle. Using that makes this puzzle easy. The formula is:
L^3/3R+1/2L^2*pi=R^2*pi
This cubic equation gives 3 roots, two of which are negative so unusable. The positive root is 15.0788
Please see http://tomlaidlaw.com/goatandsilo for more discussion.

hex has it right.
3/4 of a 45 ft. radius circle
+2*79.45/360 of 25 ft. radius circle
+Area of triangle of sides 25,25,28.28(diagonal of barn)
-1/2 barn area
Approx. 5729.5
See my complete discussion of this puzzle at http://tomlaidlaw.com/goatandsilo

3 heaviest = 35/100
3 lightest = 25/100 (5/13 of remaining => 25/65 of remaining)
So,
1 – (35+25)/100 = 40/100 weight remaining
On Average Each fish should weigh less than 1/3 of 35/100 or 12
and also weigh more than 1/3 of 25/100 or 8
Hence 4 fishes should b remaining
So a total of 10 fishes was caught.

## Paper Folding Puzzle: visual-Spatial brain exercise

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## IQ Test Question Oct 2009: What comes next

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## IQ test question: Which figure continues the series?

fafa| Profile July 28th, 2013 - 5:46 am says1

we have 3 step in each level and we should 2 for + and 1 for = in one time and 2 for = and one for + in onother one

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## The Goat Problem

Guggs| Profile July 18th, 2013 - 11:55 am saysThe area of grass the goat can eat is 5,729.52 sq ft and is made up of three separate sections:

1. 3/4 of a circle produced by the goats 45 ft tether = 4,771.30 sq ft

2. 2 segments of a circle of radius 25 ft centred at nearest corners

= 866.66 sq ft

3. 2 triangles to complete the common area eaten from clockwise and anticlockwise grazing by the goat = 91.55 sq ft

## The encircled goat puzzle

Guggs| Profile July 17th, 2013 - 2:09 pm saysThe answer to this goat in a firld problem is 115.87 m and doesn’t require the radius of the feild to be used in the equation, since once the radio of the field radius and goat tethher is computes it’s a simple mater of multiplying by 100 – see proof at link to http://www.guggs.co.uk.

## Figuring out Patterns: Grade School Kids,Grandparents?

naeem| Profile July 10th, 2013 - 7:48 pm saysb

## Guess the star colors

Bobo The Bear| PUZZLE MASTER | Profile July 5th, 2013 - 3:08 pm saysAre we sure the yellow box doesn’t already have a yellow star in it? What if the question were “How many boxes are missing their stars in this pattern?”? Would the answer be 2 or 3?

## Matrix Puzzle- Triangles & Rectangles

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## crossing the river puzzle

Sarvesh Racktoo| Profile June 15th, 2013 - 3:13 am sayshhhhhh i got it but i don’t want to reveal it lolll……

http://prntscr.com/1a1uyf

## Mystery Photo #1

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## The Tower

y3llowfl4sh| Profile June 2nd, 2013 - 7:09 am saysOnly one jailer visit them to provide them with food. the first prisoner didn’t take his food at the fifth day which is the number of cities he sees from his cell. the second will notice that and sum both the cities he sees plus the 5 which corresponds to the number of evening it took for the other to hunger strike. since each look at half of the cities so the total number would be 10

## How old?

tomlaidlaw| Profile May 31st, 2013 - 3:08 am says(year of birth)+(year of birth)/29 >1900

it doesn’t take many tries before we come up with:

1856+64=1920, so she was 44 in 1900.

## Cutting into 7 pieces

tomlaidlaw| Profile May 29th, 2013 - 2:16 am saysI think there is a rule somewhere that says at least three cuts are needed to make seven pieces. Since the paper cannot be folded or bent so after the first cut the two pieces woujld be stacked for the second cut. I’m sure I could do it with actual paper but I’m having trouble seeing it in my head only.

## The Involuting Goat

tomlaidlaw| Profile May 28th, 2013 - 11:20 pm saysL=length of rope

R=radius

As other answers have shown, this is a calculus problem. After reviewing many sites with this problem I have found an easy equation for deriving the area of the involute of the circle. Using that makes this puzzle easy. The formula is:

L^3/3R+1/2L^2*pi=R^2*pi

This cubic equation gives 3 roots, two of which are negative so unusable. The positive root is 15.0788

Please see http://tomlaidlaw.com/goatandsilo for more discussion.

## The Goat Problem

tomlaidlaw| Profile May 28th, 2013 - 11:07 pm sayshex has it right.

3/4 of a 45 ft. radius circle

+2*79.45/360 of 25 ft. radius circle

+Area of triangle of sides 25,25,28.28(diagonal of barn)

-1/2 barn area

Approx. 5729.5

See my complete discussion of this puzzle at http://tomlaidlaw.com/goatandsilo

## How Can this Be?

AHD| Profile May 19th, 2013 - 5:55 am saysTHERE GRAND FATHER ADOPTED THEM AFTER THEIR PARENTS DEAD MAYBE ?

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raybearmass| Profile May 17th, 2013 - 11:30 pm saysthe small boy, due to the position of the eyepiece on the telescope

## Graphic Puzzle with Floating Squares (Moderate Difficulty)

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## Heavy Fish

soumen023| Profile May 7th, 2013 - 5:16 am says3 heaviest = 35/100

3 lightest = 25/100 (5/13 of remaining => 25/65 of remaining)

So,

1 – (35+25)/100 = 40/100 weight remaining

On Average Each fish should weigh less than 1/3 of 35/100 or 12

and also weigh more than 1/3 of 25/100 or 8

Hence 4 fishes should b remaining

So a total of 10 fishes was caught.