Correct way to add 22 to 4 to get given value

Question

I was asked this logic puzzle in an interview.

Tell me a correct way by which adding 22 to 4 will give 2.

I asked interviewer what is the base of those numbers. He told that those are decimal numbers. I thought about it a lot, but could not find the answer. Any help would be appreciated. Thanks.

P.S. He also asked me to prove Oct 31 = Dec 25, which I did successfully. However, this question made me ask about base of those numbers. However, it is not related to question.

Answer 1

If you consider the numbers as

24 hour time

Then

$22 = 10\text{pm}\\10\text{pm} + 4 \text{ hours} = 2 \text{am}$

Answer 2

I guess the interviewer is talking about

months : if you consider 4 as April (4th month in a year) and you add 22 other months (so you go 22 months after April), you get 2 because it's February (2nd month)!

Answer 3

Another more Programmatic solution

If 4 is an unsigned 3 bit integer adding 22 to it with overflows results in 2
4 = 100
4 + 1 = 101
4 + 2 = 110
4 + 3 = 111
4 + 4 = 000
..
4 + 22 = 010 = 2

Answer 4

A more mathematical possibility is that

he is talking about modular arithmetic.

More specifically,

$22 + 4 \equiv 2 \pmod{24}$

Answer 5

A possibility is that

$22+4 = 26$ and $26$ is a two digit number.

But I hope that there is a better answer there.

EDIT:

Another possibility is

how the interviewer might have said it. What you heard is "Tell me a correct way by which adding twenty two to four will give two.". But what he might have meant can be "Tell me a correct way by which adding twenty too to four will give two.". It tells us that there is another number which has been added to 20 and 4 that should give 2. So we have $20+4+x=2$. Therefore $x=-22$. So, when we add -22 in 20 and 4 then we get 2.

Answer 6

One way that I can think of is

place 22 before 4, put a decimal between the 2's and surround the whole number with the floor function.
$\lfloor 2.24 \rfloor$

Answer 7

KoA's answer seems good to me, but I see another interpretation of the wording:

4 is a time of day and 22 is a number of hours. This time, "adding 22 to 4" means adding 22 hours to 4pm, getting 2pm, or adding 22 hours to 4am, getting 2am. This is consistent with the 24-hour clock but doesn't require it.

Answer 8

Disclaimer

As a senior software engineer, here is my egoistic view of this. I do claim it is correct or what I say are facts. You have free will to interpret this as any way you want.

Preamble

A typical candidate has an inadequate set of skills for any available position. Therefore usually for first several months, he/she is put on tasks to develop themselves and might be producing company net loss. You have to make an estimation how long would it take for this person to acquire required set of skills.

This is a simple brain teaser, you could ask from an entry level candidate. It gives an estimation of what their cognitive dissonance is like. The basic idea is if you are good/great at processing problems your knowledge base inadequacy can be overlooked.

What would I look for when asking this question

• did (s)he consider problems "solved" after finding a first working solution
• did (s)he consider that "add" can have different meanings
• did (s)he consider that "numbers" can have different contexts

I mentioned "good/great at processing problems", it is not the same as solving the problem. If the person failed you want to see how did (s)he respond to failure.

Introduction

+80% of software solution cost comes from maintenance after its development has ended. A typical enterprise code is read x10 times more than it is written. The best way to reduce the total cost is to write "clean code".

One aspect of writing "clean code" is to name things correctly. One of the simplest cases to demonstrate wording ambiguity is "add". Here are few different meanings of add (there are a lot more):

(you add 2 values)
1 + 1 = 2
(you add a value to each list value)            
{a, b, c} + 1 = {a + 1, b + 1, c + 1} 
(you add a value to start of the list)
Prepend[{a, b, c}, 1] = {1, a, b, c}
(you add a value to end of the list)
Append[{a, b, c}, 1] = {a, b, c, 1}
(you add a value to list at specified index position starting from the beginning)
Insert[{a, b, c}, 1, i] ex: {1, a, b, c} if i = 1
(you add a value to list at specified index position starting from the end)
Insert[{a, b, c}, 1, -i] ex: {a, b, c, 1} if i = 1
(you add a set of lists)
Join[{a, b, c}, {x, y}] = {a, b, c, x, y}
(you add a set of lists without duplicates)
Union[{a, b, c}, {c, a, d}] = {a, b, c, d}

In c# .net a list has a method Add for adding a single element and AddRange to add multiple elements. A single method would cause ambiguous meaning and would not be as clean.

When you implement a code on a 32bit architecture computer, there is a hardware support for bit 32-bit sequences and their basic arithmetics and logics. An integer of type int32 is implemented with 32 bits, it represents a discrete number having max value 2^31-1 and min value -2^31.

Solutions

Code examples in c# .net.

Contains spoilers.

Octo

I am not sure why his answer is voted down - it is correct.

1 baker's dozen = 13
2 baker's dozen = 26 (22 + 4)

Code :

const int BakersDozen = 13;

Value : Shows domain knowledge

manshu

Code :

public static int operator +(Manshu firstNumber, Manshu secondNumber)
    => (firstNumber + secondNumber).ToString().Count();

Value : Knows basic data types

CodeNewbie

Following code example hides (int)(22 / 10 + 4 / 10) to be 22 + 4

Code :

public static int operator +(CodeNewbie firstNumber, CodeNewbie secondNumber) 
    => firstNumber / 10 + secondNumber / 10;

Value : Knows data types / operators and maybe some functional programming

Oleg

Code :

public static int operator +(Oleg firstNumber, Oleg secondNumber) 
    => firstNumber > secondNumber ? firstNumber + secondNumber : 2;

Value : Knows about default fallbacks

Job

KoA and Menace are just sub cases of Job's general solution.

Code :

public static int operator +(Job firstNumber, Job secondNumber)
    => (firstNumber + secondNumber) % 24;

Value : Shows basic cryptography domain knowledge

Me

List that contains 22 and you add 4, now you have list containing 2 elements.

Code:

    var items = new List<int> { 22 };
    items.Add(4);

Value: Ability to read the question

Conclusion

A brain teasers during a job interviews can have valid uses. From my experience it is usually just a filler to engage the applicant.

Answer 9

adding twenty 2 to 4 will give 2.

20 * 2 + 4 = 44

So

44 is made from two 4 digits. "adding twenty 2 to 4 will give 2 (4's)".

Answer 10

22+4 = 2 x 13 (a bakers dozen)

Answer 11

Military/24 hour time
22:00 (10pm) + 4 hours = 02:00 (2am)

Answer 12

Considering 22 and 4 in hours format in a 24 hrs day cycle repesented in 24 hrs standard format

 Adding 22 hrs (10.00 pm) with 4 hrs (4.00 am) will give 22 + 4 =26 
 Pragmatically since we do not have 26 hrs we can split it as 24 + 2 which       
 in 12 hrs format is 12.00 (Midnight) and 2.00 am thus 26 hrs relatively is   
 2.00 am in 12 hrs as well as 24 hrs format

So the correct way might be adding the numbers in context with 24 hrs time format.