# Find the missing number to complete the pattern

Which number does '?' represent?

A long shot, but:

4

because:

in every row, the sum of the row is equal to the product of 2 consecutive numbers in the row. in the first row, 12=3*4, then 15=3*5, 27=3*9, 20=4*5, 12=3*4, 10=2*5

• how is 26 = 2*8 ? – Marius Apr 8 '16 at 11:30
• have corrected it now – astralfenix Apr 8 '16 at 11:32
• I just realised this could be done with multiple numbers, e.g. putting in 4 makes the sum 20, then 4*5=20. So maybe this isn't such a great answer – astralfenix Apr 8 '16 at 11:34

6

Reasoning:

The sum on row 1 + sum on row 2 = sum on row 3
$(5+4+3) + (4+3+5+2+1) = 4+3+2+9+3+5+1 = 27$
Apply the same logic for row 6 + row 5 = row 4.
$(3+2+5) + (2+1+4+3+2) = 1+3+2+?+5+2+3$
Equivalent to:
$10 + 12 = 16 + ?$
so $? = 6$

• Yep, same conclusion – tetris11 Apr 8 '16 at 14:00

My solution is quite far fetched

This is because:

By adding across the row, the sum is equal to the number at the middle multiplied by the number at the right side or the left side of the number at the middle. For example the second row has numbers 4,3,5,2,1. The sum of this row is 15. 15 is also equal to the multiplication of the middle number(5) and the number at its left (3). Apply the same logic for the row with the question mark. If the number at the right side of the question mark is taken (5) then the answer should be 4. If the number at the left is taken, the answer is 16. It seems that there are no number with 2 digits hence the answer is 4

I tried to plug it in multiple ways and these are the answers I got

1. If you add all the given numbers up you get

5 + 4 + 3 + 4 + 3 + 5 + 2 + 1 + 4 + 3 + 2 + 9 + 3 + 5 + 1 + 3 + 2 + 5 + 2 + 3 + 2 + 1 + 4 + 3 + 2 + 3 + 2 + 5 = 91

If we then divide the added total by the total given numbers:

91 by 29

to find the mean, our answer will be

3.137931034482759 which if rounded is = to 3

1. If we go back a little to elementary school we may remember finding the median and the mode.

If we take all the numbers (29 in total) and line them up from largest to smallest this is what we should get for the median:

9,5,5,5,5,5,4,4,4,4,3,3,3,3,(3),3,3,3,2,2,2,2,2,2,2,1,1,1,1

If we look for the mode the same way this is what we should get

9,5,5,5,5,5,4,4,4,4,{3,3,3,3,3,3,3,3},2,2,2,2,2,2,2,1,1,1,1

For both the median and the mode our answer is also

3