# Number Riddles: Find the Value of the Missing Number

In the tables below you will see that there are some numbers which are connected to each other.

Can you find the pattern and hence find the missing number in the table? 6 6 0 7 8 3 8 8 4 8 9 5 10 10 ?

When you get the answer, share it with your friends on Facebook and WhatsApp and see if they can solve this riddle.

## 3 Replies to “Number Riddles: Find the Value of the Missing Number”

1. OK, I looked at the site’s “solution”. What in the blazes is that kind of logic? Sum first two columns, subtract 2, and look only at the last digit? Are they complicating it as: (xi + yi – 2) mod 10 = zi ? They’re supposed to subtract 12 and check for equality; otherwise, these data points will not fall on a plane when plotted — they’ll have copies of the same solution plane of dimension 10*10*10, repeated. For example, in their solution “plane”, (6, 6, 0) is equivalent to (16, 16, 0), (11, 11, 0), (10, 12, 0), …, (1, 1, 0), (2, 0, 0), …, (xi, 2-xi+10*k, 0) for integer k. That’s a weird way of thinking, really.

2. Let the data values be grouped as a set of data points (xi, yi, zi), where i enumerates the data point.

i xi yi zi
0 6 6 0
1 7 8 3
2 8 8 4
3 8 9 5
4 10 10 ?

With only 4 known data points, we hope they fit a first-order, linear relationship, A*x + B*y +C*z + D = 0, because that’s the only equation we can solve given general, non-dependent data points. Rather than use matrix math, we’ll try something simple to see if the relationship can be determined without using “industrial-strength” math …

The reference point with i=0, (x0, y0, z0), can be compared against the other points to see if there’s any correlation:

i xi-x0 yi-y0 zi-z0
0 0 0 0
1 1 2 3
2 2 2 4
3 2 3 5
4 4 4 ?

For the given data, they show that the x delta plus the y delta is equal to the z delta.
That is, (xi-x0) + (yi-y0) = (zi-z0), for i = [0..3]. From this, we can deduce the unknown value, ? or z4, is 8.
More formally, we put in the reference point values in the equation to get: (xi-6) + (yi-6) = (zi-0) .
This simplifies to: xi + yi – 12 = zi . If we discard index i from the equation, we have: x + y – 12 = z .
In standard form, we have x + y – z – 12 = 0, and A = B = 1, C = -1, and D = -12 . So, we lucked out, eh?

1. Oh, by the way, the tables looked fine when I entered them in — the values had decent vertical alignment. However, this forum messes up the formatting and switches fonts so that everything is crooked. Sucks, eh?