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The New Number Fact Game

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Sophie.A
629229.  Sat Oct 24, 2009 4:44 pm Reply with quote

1 is the only positive integer that is neither prime nor composite.

 
principessa
629331.  Sat Oct 24, 2009 10:59 pm Reply with quote

2 is the only number whose factorial is prime

 
cherrycoke
629339.  Sun Oct 25, 2009 1:25 am Reply with quote

3 is the resin identification code used in recycling to identify polyvinyl chloride.

 
Sophie.A
629346.  Sun Oct 25, 2009 2:41 am Reply with quote

Channel 4 was launched on 2 November 1983 with the programme “Countdown”.

 
TheElephant
629356.  Sun Oct 25, 2009 4:20 am Reply with quote

5ive were rubbish.

 
Sophie.A
629363.  Sun Oct 25, 2009 4:45 am Reply with quote

6 is the only number that is equal both to the sum of its positive factors smaller than itself (1+2+3) and and to the product of its positive factors smaller than itself (1×2×3).

Obviously a number is a product of its positive factors smaller than itself if and only if it is a product of exactly two distinct prime numbers. A number which is equal to the sum of its factors smaller than itself is called a perfect number. 6 is the only perfect number that is the product of exactly two distinct primes.[/list]


Last edited by Sophie.A on Sun Nov 01, 2009 4:06 pm; edited 1 time in total

 
cherrycoke
629401.  Sun Oct 25, 2009 6:20 am Reply with quote

according to internet sources (Citation needed), seven ate nine

 
Sophie.A
629413.  Sun Oct 25, 2009 6:59 am Reply with quote

8 is considered by the Chinese to be a lucky number.

 
PDR
629415.  Sun Oct 25, 2009 7:05 am Reply with quote

In some european countries Nine is a refusenik in denial

PDR

 
bemahan
629417.  Sun Oct 25, 2009 7:10 am Reply with quote

Quote:
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1 111
1234 x 9 + 5 = 11 111
12345 x 9 + 6 = 111 111
123456 x 9 + 7 = 1 111 111
1234567 x 9 + 8 = 11 111 111
12345678 x 9 + 9 = 111 111 111
The results above are all triangular numbers in base-9.

I'm not a mathematician but think stuff like this is magical.

 
Sophie.A
629443.  Sun Oct 25, 2009 8:21 am Reply with quote

Observe that

    12 = 1 + 11

    123 = 1 + 11 + 111

    1234 = 1 + 11 + 111 + 1111

    12345 = 1 + 11 + 111 + 1111 + 11111

    123456 = 1 + 11 + 111 + 1111 + 11111 + 111111

    … etc

So

(11+1)×9 + 3 = (99 + 9) + 3 = (100-1) + (10-1) + 3 = 100 + 10 + 1 = 111

(111+11+1)×9 + 4 = (999+99+9) + 4 = (1000-1) + (100-1) + (10-1) + 4 = 1000 + 100 + 10 + 1 = 1111

… etc

Play around with these and you’re bound to find some interesting patterns (especially if you are familiar with the formula for the sum of terms of a geometric progression).


Last edited by Sophie.A on Sun Oct 25, 2009 9:38 am; edited 4 times in total

 
Sophie.A
629444.  Sun Oct 25, 2009 8:26 am Reply with quote

To continue with the game …

10 = 1 + 2 + 3 + 4

 
Vera C
629667.  Mon Oct 26, 2009 5:37 am Reply with quote

bemahan wrote:
I'm not a mathematician but think stuff like this is magical.

Then maybe you'll might like this game.

    (1) Think of a whole number, and square it.

    (2) Multiply together the number before and the number after the resulting square.

    (3) If the last digit of the new number is 4 or 9, add 3; if the last digit is not 4 or 9, add 2.

    (4) Multiply by 20 and subtract 29.

The last two digits of the final number will always be: 11

Example:

(1) 27; 27^2 = 729

(2) 728 x 730 = 531440

(3) last digit not 4, so 531440 + 2 = 531442

(4) 531442 x 20 = 10628840; 10628840 - 29 = 106288411


Last edited by Vera C on Mon Oct 26, 2009 9:30 am; edited 1 time in total

 
Sophie.A
629686.  Mon Oct 26, 2009 6:46 am Reply with quote

    (1) Think of a number other than 1 (any number except 1).

    (2) Multiply by 3.

    (3) Subtract 3.

    (4) Multiply by 4.

    (5) Divide by the number that is 1 less than than the original number you thought of.

The final answer is always 12.

 
bemahan
629694.  Mon Oct 26, 2009 7:07 am Reply with quote

1/13 = 0.076923076923076923... (rational periodic infinite decimal)
On multiplying the periodic number 76923 by successive multiples of 13, this pattern is obtained:

76923 x 13 =0999999
76923 x 26 =1999998
76923 x 39 =2999997
76923 x 52 =3999996
76923 x 65 =4999995
76923 x 78 =5999994
76923 x 91 =6999993
76923 x 104 =7999992
76923 x 117 =8999991
76923 x 130 =9999990

Is it ok that I'm looking these up, or is that cheating?

 

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