custom made puzzles

[Desardes]

Here are puzzles that i personally developed (though there maybe a case of serendipity where you may have heard a similiar one before).

1.A family I know has several children. Each boy in this family has as many sisters as brothers but each girl has twice as many brothers as sisters. How many brothers and sisters are there?



2. there is a safe with a 5 digit No. The 4th digit is 4 greater than second digit, while 3rd digit is 3 less than 2nd digit. The 1st digit is thrice the last digit. There are 3 pairs whose sum is 11. Find the number.




3. 9 cards are there. u have to arrange them in a 3x3 matrix. cards are of 4 colors.they are red,yellow,blue,green.
conditions for arrangement:
one red card must be in first row or second row.
Two green cards should be in 3rd column.
Yellow cards must be in the 3 corners only.
Two blue cards must be in the 2nd row. Atleast one green card in each row

So, any geniuses?

[joeschmoe]

when can we post answers to these? only after getting the "hats" question? :(

good riddles, btw.

[joeschmoe]

I'm answering below. don't read if you don't want to.
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1)
Children = Xboys + Ygirls

boy perspective
brothers = X-1
sisters = Y
brothers=sisters --> Y=X-1

girl perspective
brothers = X
sisters = Y-1
brothers = 2*sisters --> X=2Y-2

summing the perspectives to find the right answer:
X-2Y=-2
-X+Y=-1
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-Y=-3 --> Y=3 --> 3=X-1 --> X=4

thus, girls = 3, boys = 4. each sister has 4 brothers and 2 sisters, a 2-to-1 ratio, as required. each brother has 3 brothers and 3 sisters, an equality, as required.



2) 65292

I worked at it mathematically for a while, and then decided to assume "??292" cause it got me 2 pairs of 11, and 2 was seven less than 9. I guess I stumbled onto the answer from there.

3)
Y,R,G
B,B,G
Y,G,Y

place the yellows with the empty corner in column 3 so that you can put 2 greens in column 3. the rest falls into place.




good riddles, descardes. :)