### Brain Teasers

# Insecure

The security manager for a large company, Mr Hugh Jintellect was giving a presentation to the board regarding the new security arrangements for the building. "There will be a panel on each doorway with buttons numbered 1 to 5. To gain entry a person will have to enter a code consisting of 5 different digits by pressing the buttons in correct sequence." Jimbo spoke up and said, "To save time why don't you make it just 4 out of the 5 numbers?"

Hugh replied, "We feel that reducing the number from 5 to only 4 digits will not provide enough combinations to exclude random guesses." Why was poor Hugh sacked by the board?

Hugh replied, "We feel that reducing the number from 5 to only 4 digits will not provide enough combinations to exclude random guesses." Why was poor Hugh sacked by the board?

### Hint

How many different combinations are possible?### Answer

Hugh was sacked because he did not realise that reducing the number of buttons from 5 to 4 leaves exactly the same number of possible combinations of different buttons.For 5 buttons the number of combinations is 5x4x3x2x1= 120.

For 4 buttons it is 5x4x3x2 = 120.

After you have chosen 4 different numbers from the 5, there is only one possible fifth number remaining so it adds no extra choices to the number of combinations.

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