Balls numbered 1 through 6 are arranged in a difference triangle so that in any row, the difference between the larger and the smaller of two successive balls is the number of the ball that appears below them. Fill in the missing balls to form a difference triangle c = X:

a = 6

b = 1

c = 2

d = 5

Step-by-step explanation:

If we have a schematic design of how the triangle is supposed to be; we will have:

4 a b

c d

3

Now; we are also being told right from the question that; these balls are arranged in such a unique way that in any row; the difference between the larger and the smaller of two successive balls is the number of the ball that appear below them

i. e the difference between the larger and the smaller of two successive balls will definitely result or yield the subsequent number of ball that falls below them.

however, if we assume that a is greater than 4 and b;

then (a - 4) = c

also (a - b) = d

definitely (d - c) = 3

Since the highest number of ball is 6; then, let a = 6

so; we can replace a = 6 from the simple equations above;

(a - 4) = c

(6 - 4) = c

2 = c

c = 2

From (c - d) = 3

we can find d since we know the value of c to be = 2

(d - 2) = 3

d = 3 + 2

d = 5

Finally;

(a - b) = d

(6 - b) = 5

- b = 5 - 6

- b = - 1

Dividing both sides by - 1; we have

b = 1

We can now redraw our triangle to be:

4 6 1

2 5

3

The ball numbers are given below.

a=6

b=5

d=2

c=1