What is the number in the green block? (Given that the number in a block is the sum of the numbers in the two blocks below it.)
This is part of the series: " It's easy, believe me! "
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x be the unknown number on the second row leftmost, we observed that a = x − 6 7 and a = 2 4 0 − x − 5 3 = 1 8 7 − x . Then, equate the two equations
In figure 1, leta = a
x − 6 7 = 1 8 7 − x
2 x = 2 5 4
x = 1 2 7
It follows that 2 4 0 − x = 2 4 0 − 1 2 7 = 1 1 3 and a = x − 6 7 = 1 2 7 − 6 7 = 6 0
Fill up the other boxes as shown in figure 2.
In figure 3, let y be the unknown number on the fourth row leftmost.
In figure 4, let m be the number on the green box. We observed that m = 6 7 − y − ( y − 1 2 ) = 6 7 − y − y + 1 2 = 7 9 − 2 y and m = y − 7 − ( 4 2 − y ) = y − 7 − 4 2 + y = 2 y − 4 9 . Equate the two equations
m = m
7 9 − 2 y = 2 y − 4 9
7 9 + 4 9 = 4 y
y = 3 2
It follows that,
m = 7 9 − 2 ( 3 2 ) = 1 5
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We call the values in the three empty blocks in the bottom row α , β and γ . Then we add our way up the pyramid as shown below:
Then from the pairs of blocks beneath the three red blocks in the top and middle rows, we get the equations
1 2 0 + 2 α + 4 β + 2 γ 1 2 + 2 α + β β + 2 γ + 1 8 = 2 4 0 = 6 7 = 5 3 ⟹ ⟹ ⟹ α + 2 β + γ 2 α + β β + 2 γ α + β + γ β = 6 0 = 5 5 = 3 5 = 4 5 = 1 5 ( 1 ) ( 2 ) ( 3 ) ( 4 ) [ Half of sum ( 2 ) + ( 3 ) ] [ ( 1 ) − ( 4 ) ]