a thinker/ puzzle--- improving your algebra skills---geometry?

Question

place 4 different numbers in the bubbles at the vertices of the pyramid so that the two numbers at the ends of each edge or diagonal add up to the number on that edge---the picture shows a square like a base ball field. Home would be B first base A second D and third C. There`s a line that meets from B to D running vertical with the number 53 and a line from A to C running horizontal with the number 44. The number between A anb B is 56, the number between B and C is 60, the number between C and D is 41, the number between D and A is 36.
* if u have any kind of help or opinion or even a guess please let me know thanx.

Answer 1

If I'm understanding the problem, you have a set of 6 equations with 4 unknowns:
b+d=53
a+c=44
a+b=56
b+c=60
c+d=41
d+a=36

Unfortunately, the equations are in conflict and no solution can be derived. If we make d+a=37, instead of 36, you can derive the following solution:
a=20
b=36
c=24
d=17

Answer 2

at first glance, there is no solution to this puzzle.

" B to D running vertical with the number 53 "
... translates to :

B + D = 53
A + C = 44
- - - - - -- -- - - adding:
A + B + C + D = 53 + 44 = 97

now using the same 'translation'-scheme on the
"base-paths":

A + B = 56
B + C = 60
C + D = 41
D + A = 36
- - - - - -- - adding up,
A + B + B + C + C + D +D + A =
2(A + B + C + D) = 56 + 60 + 41 + 36 = 193

problem is that 97 * 2 = 194, ( not 193)

you may have some bad data ...

Answer 3

A + B = 56
A + C = 44
A + D = 36
C + D = 41

From the first equation we get that A = 56 - B. When you substitute this into equations 2 and 3, and solve for C and D respectively you get the following.

A + C = 44
(56 - B) + C = 44
C = B - 12

A + D = 36
(56 - B) + D = 36
D = B - 20

Now, plug the values of C and D into equation 4 and solve for B.

C + D = 41
(B - 12) + (B - 20) = 41
2*B - 32 = 41
2*B = 73
B = 36.5**************solution for B

Now that you have B you can simply use the values on the lines to figure out what A, C, and D are.

(A = 19.5, C = 24.5, and D = 16.5).

Answer 4

Quick_silver_707, your B + D adds to 61, not 60 as required.

I think the answerers who say there is no solution are correct.

There is something very suspicious about a problem that gives way more information than is needed to solve.

Answer 5

This puzzle has no solution; there is no way to satisfy all the conditions of the problem.

Answer 6

Hi,

A = 19
B = 37
C = 25
D = 16

Answer 7

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