my first puzzle,,,,let's play with puzzles
The figure below is a number pyramid. The number in each square is the sum of the numbers in the two squares on which it rests (except for the squares in the bottom row). As you can see some of the numbers are hidden.
Determine the exact value of the hidden number in the square labeled with the question mark. It needn't be a whole number.
good luck
select space below if you want to see my answer
23 2/3
Write D in the centre box on the bottom, then fill in all the empty cells in terms of D and what is
given. Then the relationship between the second from top row and the top row gives an equation
from which D can be found. Having found D all the cells may now be completed including the one
marked with a ?.
RonL
Select the text below to show my answer.
If we turn it all upside down, it's like almost like Pascal's triangle. If all the numbers in the bottom row except from the one would be zero, for example, the number in the top square would be [tex]5\choose{1}[/tex]. But since we now have five different bottom row squares, of which one is unknown (let's call that number a), which all affect the top square, the number in the top square is now a linear combination of five different combination quantities (if I may call it so). The equation for the number in the top square would be:
[tex]81 = 1\cdot {5\choose{1}} + 2\cdot {5\choose{2}} + a\cdot {5\choose{3}} + 3\cdot {5\choose{4}} + 4\cdot {5\choose{5}}[/tex]
Then we have the equation for the square with the question mark in it, and that equation looks like this:
[tex]? = 2\cdot {3\choose{1}} + a\cdot {3\choose{2}} + 3\cdot {3\choose{3}}[/tex]
It seems like my previous post where incorect, since I once again forgot to use zero indexing inside the parenthesis. So, it really should look like this:
If we turn it all upside down, it's like almost like Pascal's triangle. If all the numbers in the bottom row except from the one would be zero, for example, the number in the top square would be . But since we now have five different bottom row squares, of which one is unknown (let's call that number a), which all affect the top square, the number in the top square is now a linear combination of five different combination quantities (if I may call it so). The equation for the number in the top square would be:
Then we have the equation for the square with the question mark in it, and that equation looks like this:
So, first solve what is, then you solve what is ( depends on ) to get what should be in the square. This I hope will be right, but I still haven't tested it. contains the answer.