# Somebody hacked my calculator

Harvey the hacker struck again. After powering on my calculator, I entered the Keystrokes in the order shown below. Instead of the Expected Result, I got the Hacked Result.

What will be the last Hacked Result?

Update / Hints:

As mentioned in the comments, these are important observations:

• Rows 2 and 9 have the same Keystrokes, but different Hacked Results
• The Hacked Result is always bigger than the Expected Result

Once you know the answer, the Hacked Result can be calculated with simple math by doing this:

Tapping your finger on the grid

$$\begin{array}{|c|c|c|} \hline \textbf{Keystrokes}&\textbf{Expected Result}&\textbf{Hacked Result} \\ \hline 2+4*2-3= & 7 & 16 \\ \hline 8/4+3-1= & 4 & 14 \\ \hline 2-6/3+8/4= & 2 & 15 \\ \hline 4*(2+2)= & 16 & 28 \\ \hline 7-(2-3)*3= & 10 & 25 \\ \hline 5+0/1+(5-3)= & 7 & 25 \\ \hline 6/3*3= & 6 & 19 \\ \hline (5-3)*5-3= & 7 & 25 \\ \hline 8/4+3-1= & 4 & 21 \\ \hline (3+7)/2= & 5& 23 \\ \hline 9-2*(3+1)= & 1 & ? \\ \hline \end{array}$$

CSV version:

Keystrokes,Expected Result,Hacked Result
2+4*2-3=,7,16
8/4+3-1=,4,14
2-6/3+8/4=,2,15
4*(2+2)=,16,28
7-(2-3)*3=,10,25
5+0/1+(5-3)=,7,25
6/3*3=,6,19
(5-3)*5-3=,7,25
8/4+3-1=,4,21
(3+7)/2=,5,23
9-2*(3+1)=,1,?

• How could 8/4+3-1 equals 14 or 21 in the example? (in row 2 & 9) – Conifers Jul 26 at 8:31
• @Conifers "How could 8/4+3-1 equals 14 or 21 in the example? (in row 2 & 9)" That is an important observation. – FlanMan Jul 26 at 10:42

It looks like the answer is

22

Explanation

result = expected result + number of symbols + number of the expression (row of the table)
so for the last expression is $$1 + 10 + 11 = 22$$

• Impressive, well done ^.^ – TinyDoowy Jul 29 at 6:47

I have maybe an answer, let me check.

I think he changed the operator like here :

(3+7)/2 = 5 give

(3*7)+2 = 23 as unexepected, so + become * and / become +

Taking another example : 8/4+3-1 = 4

8+4*3?1=21 so - become +

A last one to confirm : 5+0/1+(5-3)=7 become

5*0+1*(5+3) = 8

And it didn't work. I will post my answer anyway in case it can help someone later.

• Just checked programmatically: no operator replacements will solve the first line. It must be something else. – Birjolaxew Jul 26 at 8:53
• @Birjolaxew I also checked number replacements, but i didn't try both number and operators. I also thought about priority changes, but not working. – TinyDoowy Jul 26 at 9:16
• I think of something else, the hacked number are way bigger than regular result, maybe we should use this information in our calculation ? – TinyDoowy Jul 26 at 9:23
• @TinyDoowy "the hacked number are way bigger than regular result". That is an important observation. – FlanMan Jul 26 at 10:40