A "Number Pyramid" is composed of ten different numbers ( usually 0 - 9 ) with four rows. ONE EXAMPLE of a Number Pyramid is as follows:

      0

    1   2

  3  4   5

6  7   8   9

Given the clues below, determine the composition of a new Number Pyramid.

1) The sum of the two numbers in the second row is 11.

2) The sum of the numbers in the bottom row minus the sum of the numbers in the third row equals 10.

3) The rightmost numbers in the four rows must sum to 18.

4) The middle number in the third row minus the leftmost number in the second row should equal 4.

5) Subtracting the top number in the Pyramid from the rightmost number in the second row leaves 4.

6) In the bottom row, the leftmost number is greater than the second number from the left, while the rightmost number is greater than the second number from the right.

For bonus marks, which of the above clues (if any), are not necessary in order to construct the pyramid?

There is only (you can see that analysing solution wih description) one pyramid meeting all requirements from all he clues given:
4
3 8
2 7 1
9 6 0 5

As I show you below there it is possible to built another pyramid when you ommit any of the clues.

I.
Without clue 1
0
1 4
2 5 8
9 7 3 6

II.
Without clue 2
4
3 8
6 7 1
9 2 0 3

III.
Without clue 3
4
3 8
1 7 2
9 6 0 5

IV.
Without clue 4
4
3 8
7 2 1
9 6 0 5

V.
Without clue 5
0
2 9
5 6 1
7 4 3 8

VI.
Without clue 6
4
3 8
2 7 1
6 9 0 5

As you can see to get the only answer to the problem of building pyramid like in the task above you need all the clues.

Answer:
All the clues are needed in order to construct pyramid.

Posted by Rafal on 2004-09-05 11:13:53