Logic Q

[Amina-DZ]

Originally posted by Flora
Hum...I'll use light, it's cheaper ....better it's free

and hassle-free too

[Flora]

Hum we're not getting anywhere. I guess I will hire an interior designer

[phylay]

Originally posted by Amina-DZ

The sum isn't 7.11 and the number of items should be 4.

And yes it has to be exactly 7.11.

You might solve it at 7am

I've found many possible solutions (even if I think there's a finite number of them).

Here's the nearest one:
1.00 + 3.00 + 1.77 + 1.34 = 7.11
1.00*3.00*1.77*1.34 =~ 7.11 (actually 7.1154 but the clerk in a marketing action approximates to 7.11 and not 7.12 )

[Shotokan_Karate]

The Pentagram

Well done!

Phylay, you got it...except the question is the ratio AB/BC which of course is the reciprocal of 0.618034 which is 1.618034.

Damya, that's the one!

Dear rival! You were sooooo close!



Here's the given solution:

Construct another regular five-pointed star as shown in the diagram. Since both are regular stars, AB/BC = AD/DB.



Let AB be of unit length and AD = BC = x (so DB = 1 - x)
Then: AB/BC = AD/DB so: 1/x = x/(1-x)
So: x^2 + x - 1 = 0, x = -1/2 + 1/2 sqroot5 = 0.618034, and the ratio of AB to BC is the reciprocal of 0.618034 which is 1.618034.

[Shotokan_Karate]

Originally posted by Amina-DZ
In a 7-11 shop, a customer selected four items to buy. The check-out clerk says that he multiplied the costs of the items and obtained exactly 7.11, the very name of the store! The customer calmly tells the clerk that the costs of the items should be added, not multiplied. The clerk then informs the customer that the correct total is also $7.11.
What are the exact costs of the 4 items?

Phew!! Not an easy one!

I'm thinking...

[Shotokan_Karate]

Originally posted by phylay
I've found many possible solutions (even if I think there's a finite number of them).

Here's the nearest one:
1.00 + 3.00 + 1.77 + 1.34 = 7.11
1.00*3.00*1.77*1.34 =~ 7.11 (actually 7.1154 but the clerk in a marketing action approximates to 7.11 and not 7.12 )

mmm....I doubt it! I reckon for both the sum and the multiplication of the costs to equal exactly 7.11 then there can only be one solution to the problem.

[phylay]

Originally posted by Shotokan_Karate

mmm....I doubt it! I reckon for both the sum and the multiplication of the costs to equal exactly 7.11 then there can only be one solution to the problem.

You have and a non linear system with 4 variables. Nothing proves the solution is unique. Actually many solutions can be found but most of them include negative costs I found two exact positive solutions but given that we use only 2 decimals, I had to approximate and the one above is the nearest