The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 124 different signs. If the company used 122 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 124 signs?

I assume that the code can consist of 2 similar sings (AA, BB)

"We know that 2 signs are unused" so now observe the conditions

1) 2 signs can be themselves as 2!=2 codes, plus 2 i.e.,(AA and BB), 4 overall.

2) With 2 unused signs we have 2 different first signs and 2 later ones ( 2*2=4).
We have another 122 signs to be the first or the second sign of the code.
Combinely we have 4*122 possibilities.

So, (122*4)+ 4 = 492.

totally 492 possible codes can be created
10 years agoHelpfull: Yes(11) No(3)
492 more signs
10 years agoHelpfull: Yes(4) No(8)
The phone company already created 122*122 area codes, now it can create 124*124. 124^2-122^2=(124+122)(124-122) = 246*2 = 492 additional codes.
9 years agoHelpfull: Yes(4) No(0)
122+122+1=245 more
10 years agoHelpfull: Yes(3) No(7)
ans will be 492
10 years agoHelpfull: Yes(2) No(2)
2^124-2^122
10 years agoHelpfull: Yes(2) No(2)
124*124 - 122*122=492
8 years agoHelpfull: Yes(0) No(0)

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