Puzzles- contd

STRESS RELIEF

When I posted the 4x4 dot matrix puzzle I expected soutions with only horizontal and vertical lines! :) Kirukan gave one. There are others. Can you find them? You will be surprised to see how simple they are!

Benny Lava : Here is the correct solution for 3x3 dot matrix ! :)



.....o.....o.....o <- Start here at (3,3)

.....o.....o.....o

.....o.....o.....o

.................................



line 1...................... (3,3) to (0,3) Connects the dots in top row

line 2...................... (0,3) to (3,0) Connects the dots below the main diagonal in the matrix of dots

line 3....................... (3,0) to (3,2) Connects the bottom two dots in the last column

line 4........................ (3,2) to (1,2) Connects the three dots in the middle row

line 5....................... (1,2) to (1,1) Connects the bottom two dots in the first column

This is similar to the solution for the 4x4 dot matrix.

(There is a pile of small sheets in front of the monitor . I picked the wrong one earlier. I have already given you a few of the other possible solutions with 5 lines! :) )

I hope all of you visiting this thread had enough stress relief! :)

Here is another problem to use what a Greek mathematician discovered:

A five meters long ladder is leaning against a wall. A cubic box ( 1m x 1m x 1m) is against the wall. One edge of the cube touches the ladder and one side of the cube touches the wall with another side on the ground. That is, the one meter cube box fits snugly in the gap between the ladder and the wall sitting on the ground.

What is the distance of the foot(base) of the ladder from the wall?

Close to 400 views! But, no solution yet! :) Time to assemble all information to solve the puzzle!

1. Draw a diagram - cross section

2. The ladder leaning against the wall makes a triangle with the wall and the floor as sides. Hypotenuse has a length of 5 meters.

3. Inside the triangel is a square of side 1 meter. The square divides the large triangle into two small triangles.

4. One triangle sits on the square. That is the length of a side is 1 meter

5. The other small triangle is on the side sharing a side with the square. That is one side of the triangle is 1 meter.

6. The bases ( horizontal sides) of the two small triangles are parallel to each other(and parallel to the ground) .

7. The other sides of the small triangles are also parallel( and parallel to the wall)

8. There must be something special about the two small triangles! :)

9. We learnt a few things in geometry and there is Pythogorean theorem!

Now try! :)

Hint: you have to use one unknown - either the horizontal side of the triangle on the side of the square and relate to the vertical side of the other small triangle or vice versa ! :)

what, this has not been solved even after 10 days?
this doesn't look that much difficult.

i think 2 answers possible for dis.
4.84m and 1.26m?
just a rough calculation.
if wrong, tell me. will once again try it thinking out of box.

GP:
Which one makes sense if you are doing something on the wall? It will help others if you explain how you solved it! :)

I hope it is not by trial and error ! :lol:

let base of the bigger triangle be 'b' and height be 'h'.
Relating the two small triangles,
(h-1)X(b-1)=1X1 => hb=h+b => h=b/(b-1) --> Eqn I
According to Pythogoras,
h^2+b^2=25 --> Eqn II
Solving Eqn I and II,
(b/(b-1))^2+b^2=25 => b^2(1+1/(b-1)^2)=25
Solving the above eqn we can find the value of 'b' and hence 'h'.
of course i used excel spreadsheet for solving the last eqn.

Correct! :)

1.260 is the right answer. With the other length you won't need a ladder! If one is the base the other will be the height. You don't need a ladder for a height of 1.26 m ! :)

In case people are wondering equation one is from the fact that the two small triangles are similar! :)

If nobody posts the next puzzle I will post one soon! :)


How do you solve it without writing a script?

high school maths la indha diagram padicha nyabagam konjam irundhuchu, especially that relationship between smaller triangles.
idhukku script, screenplay yellAm thEvai padala.
it was a nice stress reliever. :wink:

Quote:

---

Originally Posted by GP

of course i used excel spreadsheet for solving the last eqn.

---

How do you solve it without a spreadsheet/script?

Hint: Let (b-1) = x, the distance between the square and the ladder along the floor. Rewrite the last equation with x. Express the 4th degree equation as a square of a quadratic equation. Now, you won't need a spreadsheet/script! :) A simple $4 calculator will do or an approximation! :)

( These puzzles are from practice IQ tests where a laptop is not allowed! :lol: )