The consecutive number game.

861 is the 41st triangular number.

41 + 40 + 39 + … + 3 + 2 +1 = 861

Two quick ways to compute a selected triangular number:

  1. Multiply the largest number n of the series (in this case, 41) by the midpoint between nand 1.

41 x 21 = 861

  1. Add n to 1, then multiply that result by half of n.

41 + 1 = 42
41/2 = 20.5
42 x 20.5 = 861

&nbsp &nbsp &nbsp &nbsp &nbsp 862
&nbsp Factors into 431 * 2
&nbsp Notice that the digits 1 through 4 are used just once.

&nbsp &nbsp &nbsp &nbsp &nbsp 863
&nbsp The 150th Prime Number

&nbsp &nbsp &nbsp &nbsp &nbsp 864
&nbsp Factors neatly into: 2[sup]5[/sup] * 3[sup]3[/sup]
&nbsp = 32 * 27

&nbsp &nbsp &nbsp &nbsp &nbsp 865
&nbsp =2² +3² +4² +5² +6² +6³ +7² +8² +9² +10² +11² +12²
&nbsp =4 + 9 + 16 + 25 +36 + 216 +49 +64 +81 +100 +121 + 144

RFC 866

&nbsp &nbsp &nbsp &nbsp &nbsp 867
&nbsp 17² * 3
&nbsp = 289 * 3

&nbsp &nbsp &nbsp &nbsp &nbsp 868
&nbsp Another neat factorization 2 * 2 * 7 * 31

&nbsp &nbsp &nbsp &nbsp &nbsp 869
&nbsp Factors into two 2 digit prime numbers 11 * 79

&nbsp &nbsp &nbsp &nbsp &nbsp 870
&nbsp This is the product of 2 consecutive numbers
&nbsp 870 = 29 * 30

&nbsp &nbsp &nbsp &nbsp &nbsp 871
&nbsp 871 is the product of 2 two digit prime numbers:
&nbsp 871 = 13 * 67

Photos of a home at 872 Amanda Drive, James Island

&nbsp &nbsp &nbsp &nbsp &nbsp 873
&nbsp The sum of a perfect square and cube
&nbsp = 12[sup]2[/sup] + 9[sup]3[/sup]
&nbsp = 144 + 729

&nbsp &nbsp &nbsp &nbsp &nbsp 874
&nbsp Factors into 2 * 19 * 23

&nbsp &nbsp &nbsp &nbsp &nbsp 875
&nbsp Another interesting factorization:
&nbsp 875 = 5[sup]3[/sup] * 7
&nbsp = 5 * 5 * 5 * 7
&nbsp = 25 * 35

Louis the German, King of East Francia, died in the year 876 AD.

&nbsp &nbsp &nbsp &nbsp &nbsp 877
&nbsp A prime number (the 151st to be exact)

Studio 878 provides dance lessons to the people of Cape Cod.

Dean Smith’s 879 wins make him the winningest college basketball coach ever.

There are 880 4 x 4 magic squares.