Math Is Fun Forum

tony123

Member

Registered: 2007-08-03

Posts: 229

Determine the integer n with the properties

Determine the integer n  with the properties :

1.)n is a prime less than 6000

2.)The number formed by the last two digits of n  is < 10

3.)If the decimal digits of n  are reversed to obtain N , then N - n = 999

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Determine the integer n with the properties

2) means that the second last digit must be 0, so you have a number of the form

ab0c (not multplication) = 1000a+100b+c (a,b,c are integers in the range 0-9)

3) the reversal N is c0ba = 1000c+10b+a

N-n = 1000(c-a)-100b+10b+(a-c) = 999

a-c = 9
b = 9

hmmm. im a bit lost with it now, the negatives are messing things up in my head here

Last edited by luca-deltodesco (2007-11-16 22:23:23)

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JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Determine the integer n with the properties

Hence N is the number obtained from n by adding 1 to the first digit and subtracting 1 from the last digit of n. (NB: n doesn’t end with two 0s otherwise it wouldn’t be prime.)

∴ c = a+1, b = 0.

Also, c (being the last digit of a 4-digit prime) must be 1, 3, 7 or 9. But c can’t be 1, 7 or 9 because the first digit of n is c−1 and n is < 6000. This leaves only c = 3.

Hence:

Last edited by JaneFairfax (2007-11-17 02:20:37)

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Determine the integer n with the properties

Practical arithmetic tip:

Adding 999 to a 4-digit number whose last digit is not 0 is the same as adding 1 to the first digit and subtracting 1 from the last digit.

Similarly for adding 99, 9999, 99999, etc. That’s how I add up my shopping cost to find out how much to pay before going to the cashier’s (just to make sure I don’t overspend). If something costs 99p and I add it to my shopping basket, I mentally add £1 and deduct 1p from my shopping total.

Example: £5.34 + 99p = £5.34 + £1 − 1p = £(5+1).(34−1) = £6.33

And this can be modified to use on more complicated sums:

£5.34 + £2.93 = £5.34 + £3 − 7p = £(5+3).(34−7) = £8.27

Last edited by JaneFairfax (2007-11-17 01:09:13)