Car Registration

[Dee-M-See]

To remember my four digit pin number, I squared the numbers on my car registration plate,by coincidence the last two digits of my pin number turnout to be my cars registration number can you work out my pin number?

[shammydodger]

5776

[Dee-M-See]

Thank you shammydodger very prompt answer I owe you a Pint

[shammydodger]

Go to the blood bank next time they're in town and deposit a pint of A+. I'll redeem it later!

[crofter]

What a neat problem and there are fewer options than you would think!

The answer 5776 only works because 76^2 = 5700 + 76

In general, if your two-digit car number is c, then c must satisfy c^2 = 100d + c or c(c-1) = 100d for some other number d. That is, the product c(c-1) MUST generate a factor of 100 = 4x25.

This means that c or (c-1) must be 25 or 50 or 75 or 100. Discard 25 (it squares up to give only a three-digit number), discard 50 (its square ends in 50) and discard 100 (it was not permitted? to have a registration number 00). You are then left with two cases to check, namely c =75 or c-1 = 75 (c = 76).

The rest is history - and down to shammydodger!

[snoozy]

I am in awe of you both. I had to resort to a spreadsheet to fully understand this puzzle.

[earthakitten]

crofter ... I am truly amazed by you..do you ever enter the quizzes etc or spend your waking hours helping others ????? xx

[crofter]

earthakitten, I am a mathematician by profession, so I am naturally attracted to number puzzles and try to use equations to obtain a solution rather than trial and error.

For Quizzes, I enter those set by Rainbow, Edmund Marshall, Matlock and a few of the local ones. I have had my share of "wins".

I often work at a desk for most of the day and tune into AnswerBank for coffee breaks and lunch times (such as now). I help as often as I can - but the competition can be fierce. There's some very sharp people out there with quick brains and even quicker typing fingers!