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 Question from Jason, a student: Hi, I can't seem to open my locker cause I forgot the combination, the numbers are 1-8 Without repeat for 4 number for example 1234 or 2345 for numbers 1-8 without any repeat.

Hi Jason,

Reading the digits from left to right you have 8 choices for the first digit, and once that digit is chosen you have 7 choices for the second digit. Thus you have $8 \times 7$ choices for the first two digits. Once these are chosen you have 6 choices for the third digit and 5 for the final digit and thus you have $8 \times 7 \times 6 \times 5 = 1680$ possible combinations. I am not going to list them for you but I will show you how to try each possibility in an orderly fashion.

If you think of the four digit combinations as four digit numbers you can list them in order.

1234, 1235, 1236, 1237, 1238

There is no 9 or 0 so the next numbers are

1243, 1245, 1246, 1247, 1248

Continuing I get

1253, 1254, 1256, 1257, 1258

1263, 1264, 1265, 1267, 1268

1273, 1274, 1275, 1276, 1278

1283, 1284, 1285, 1286, 1287

These are all the possible lock combinations with 12 as the first two digits. Continuing the list in numerical order I get

1324, 1325, 1326, 1327, 1328

and so on.

If you continue in this way it shouldn't take too long to go through the 1680 possible combinations.

I hope this helps,
Harley

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