Guessing a lock combination

Suppose you have a lock and you don't know the combination to it.
Each field can contain any number ranging from 0 through 9. How many combinations can there possibly be? How to find the right combination?

One way to find the right combination is by trying all the possible combinations until the right one is found. Since the maximum value for each field is 9 and in this case we have 4 fields we can count from 0000 to the maximum value which is 9999 to generate all the possible combinations.

To know how many possible combinations there are, simply take the maximum value and add 1 to it. In this case 9999 + 1 = 10000. The 1 is simply because 0000 also counts as a possible combination.

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Hexadecimal to Decimal

To convert a hexadecimal to decimal all we have to do is do is perform the opposite procedure we used to convert to hex. In this example we will turn back the number that we used here(#35) into decimal. First we must use the table to get back again the Remainder Decimal value Hex Equivalent 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 A 11 B 12 C 13 D 14 E 15 F Note: each hexadecimal digit represents the Remainders found when converting the number from decimal to hexadecimal Now revert the Process by performing these simple steps: Use the table above to find the decimal equivalent of each Remainder in the case of #35 is 3 5 Multiply each of the remainders(decimal equivalent of each hex character) by 16 to the power of "n" where "n" is the position of each character. The position of the character is found by counting from right to left and starting the count on 0 rather than 1. Note: the

Counting in Hexadecimal

When searching for how to convert decimal numbers to hexadecimal it may seem like a daunting task. Until you learn about modulo . The easiest way for me to count in Hex is by counting in decimal and converting to Hexadecimal using the modulo operator(like a programmer). First you divide the decimal number by 16 Math.floor() the Division Result Find the Division Remainder using modulo Divide the number of your Division Result by 16 Repeat the previous steps until your Division Result is 0 For this example we will use the decimal number 53 Divide Division Result Division Remainder 53 / 16 Math.floor(3.3125) = 3 53 % 16 = 5 3 / 16 Math.floor(0.1875) = 0 3 % 16 = 3 We take the remainders going from the latest remainder to the one we got first. In this case 3 5 (the order is important). Then we use this table to translate the remainders into hex Decimal value Hex Equivalent 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10

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