Five hundred begins it, five hundred ends it,
Five in the middle is seen;
First of all figures, the first of all letters,
Take up their stations between.
Join all together, and then you will bring
Before you the name of an eminent king.[/QUOTE]
That was already posted somewhere at the beginning of this thread...
You have nine coins. One of the nine is counterfeit. The counterfeit coin can only be
distinguished by weight---it is heavier than the rest. Using a balance scale only twice, find the counterfeit coin.
1.) Divide the 9 coins into groups of three.
2.) Scale 2 of the groups, if they are even, the counterfeit coin is in the 3rd group, if one of them is heavier than the other, the coin must be in that group, obviously. So now we know the group our coin is in.
3.) Scale 2 coins of the three, if one is heavier than the other, there ya go If they are even, the remaining coin is the counterfeit. <--
Sabrina gave Samantha as many dollars as Samantha started out with. Samantha then gave Sabrina back as much as Sabrina had left. Sabrina then gave Samantha as back as many dollars as Samantha had left, which left Sabrina broke and gave Samantha a total of $80.00. How much did Sabrina and Samantha have at the beginning of their exchange?
--> Oooh I was very wrong, I see now OK do it properly now:
Sabrina's starting amount: x
Samantha's: y
1.) x; y
2.) Sabrina gave Samantha as many dollars as Samantha started out with.
x-y; 2y
3.) Samantha then gave Sabrina back as much as Sabrina had left.
2*(x-y); 2y-(x-y) = 3y-x
4.) Sabrina then gave Samantha as back as many dollars as Samantha had left, which left Sabrina broke and gave Samantha a total of $80.00.
2*(x-y)-(3y-x); 2*(3y-x) ==>
a.) 2x-2y-3y+x = 0 --> 3x-5y = 0 --> 3x = 5y
b.) 6y-2x = 80 --> 3y-x = 40 --> x = 3y-40
==>
3*(3y-40) = 5y
9y-120 = 5y
4y = 120 --> y = 30; x = 50
Check:
1.) 50; 30
2.) Sabrina gave Samantha as many dollars as Samantha started out with.
20; 60
3.) Samantha then gave Sabrina back as much as Sabrina had left.
40; 40
4.) Sabrina then gave Samantha as back as many dollars as Samantha had left, which left Sabrina broke and gave Samantha a total of $80.00.
0; 80
[QUOTE=Ravager]There is such a thing as overthinking a riddle, Brynnie . Nice algebraic solution though .
If your answer is 0, 80 then it's wrong. Otherwise explain your answer to me. All that maths confused me... [/QUOTE]
Sabrina started with 50, and Samantha with 30 as I concluded, for short explanation see the "check" part
Overthinking? Yeah, common problem for me, I admit that. But in this case, is there a solution (apart from trying some combinations and being lucky) that doesn't involve mathematical calculations...? I mean, can you answer the riddle without translating the problem into equations?
I suppose algebra is the best way to solve the riddle. It just confused me somewhere along the line
Debbie promised to take her daughter Becky shopping on the day before the fourth day after the day after tomorrow. If today is Sunday the 3rd. On what day and date will Becky take Debbie shopping?
[QUOTE=Ravager]Debbie promised to take her daughter Becky shopping on the day before the fourth day after the day after tomorrow. If today is Sunday the 3rd. On what day and date will Becky take Debbie shopping?[/QUOTE]
thursday the 7th
Zombies are not real! The Government is still doin Human trails!
Have you ever wondered why, in a dream you can touch a falling sky? Or fly to the heavens that watch over you. - Godsmack
