# Find the missing number in the 5 by 5 table

What is the missing number in the matrix? I was asked this in a job interview for quant finance. $$\begin{bmatrix} 1&9&3&13&260\\ 5&8&3&0&664\\ 8&18&21&25&1454\\ 4&11&6&3&?\\ 10&20&30&40&3000 \end{bmatrix}$$

Answer is one of the following: 1639, 1738, 1638, 1640

• Are you sure the second row is correct? There is a (mathematically) simple pattern which all of the other rows follow - should its final column actually show 98?
– Stiv
Commented Jan 31, 2022 at 22:04
• This is what it is, I have taken a photo let me add the options too, that might give a clue. Commented Jan 31, 2022 at 22:12
• You were asked this in a job interview? I have trouble understanding. What role did you interview for where this question is possibly appropriate?
– mafu
Commented Feb 2, 2022 at 4:56
• @mafu Yes, I don't want to say where, because it might reveal my identity to them. It is a quant finance job. In this field they like to ask a lot of brain teasers in a very short amount of time as the initial screening to weed out most of applicants. Commented Feb 2, 2022 at 5:04

## 2 Answers

1638

Reasoning:

In the odd rows the number in the last column is the sum of the other numbers' squares, while in the second row this pattern applies to the cubes, so I think the missing number is $$4^3 + 11^3 + 6^3 + 3^3 = 1638$$

Given the possible options, I believe the most appropriate answer is:

1638

Since:

For odd-numbered rows, if you square each of the numbers in the first four columns and sum them together, you produce the number in the fifth column.

e.g. 1 squared + 9 squared + 3 squared + 13 squared = 1 + 81 + 9 + 169 = 260

However, row 2 does not obey this rule - instead, if you cube each of the numbers in its first four columns and sum them together, you produce the number in its fifth column:

5 cubed + 8 cubed + 3 cubed + 0 cubed = 125 + 512 + 27 + 0 = 664

Although we have very few data points, this might suggest that this 'cubing' rule should be applied to all even-numbered rows, including row 4 (the one of interest to us). This means our question mark should be replaced by 1638, since:

4 cubed + 11 cubed + 6 cubed + 3 cubed = 64 + 1331 + 216 + 27 = 1638

• Well now I don't know which one to accept both came at the same time with the same solution! Commented Jan 31, 2022 at 22:22
• @user127776 Whichever one you like! :)
– Stiv
Commented Jan 31, 2022 at 22:22
• I am accepting the other one, since the user is new they might need it the most! Commented Jan 31, 2022 at 22:24