The New Number Fact Game

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 629229.  Sat Oct 24, 2009 4:44 pm 1 is the only positive integer that is neither prime nor composite. 629331.  Sat Oct 24, 2009 10:59 pm 2 is the only number whose factorial is prime 629339.  Sun Oct 25, 2009 1:25 am 3 is the resin identification code used in recycling to identify polyvinyl chloride.  629346.  Sun Oct 25, 2009 2:41 am Channel 4 was launched on 2 November 1983 with the programme Countdown. 629356.  Sun Oct 25, 2009 4:20 am 5ive were rubbish. 629363.  Sun Oct 25, 2009 4:45 am 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 629401.  Sun Oct 25, 2009 6:20 am according to internet sources (Citation needed), seven ate nine 629413.  Sun Oct 25, 2009 6:59 am 8 is considered by the Chinese to be a lucky number. 629415.  Sun Oct 25, 2009 7:05 am In some european countries Nine is a refusenik in denial PDR bemahan
629417.  Sun Oct 25, 2009 7:10 am 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. 629443.  Sun Oct 25, 2009 8:21 am 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 629444.  Sun Oct 25, 2009 8:26 am To continue with the game  10 = 1 + 2 + 3 + 4 629667.  Mon Oct 26, 2009 5:37 am 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 629686.  Mon Oct 26, 2009 6:46 am (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 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? Page 1 of 426
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