More Fun Facts With Num3ers

1 + 3 + 1 = 1^2 + 2^2

1 + 3 + 5 + 3 + 1 = 2^2 + 3^2

1 + 3 + 5 + 7 + 5 + 3 + 1 = 3^2 + 4^2,

etc...

153 is the sum of the first five factorials: 1! + 2! + 3! + 4! + 5! = 153

The 26 letters of the alphabet can make 40,329 * 10^22 different combinations

1961 was the most recent year that could be written upside-down and rightside-up and appear the same. The next year with the same properties is 6009

If you change a $5 bill into all the possible ways (cents,nickels,dimes,quarters,halves and dollars) it would require: 2,305,843,009,213,693,951 different changes

Recreation with the 8x table:

1*8=8 (8);

2*8=16 (1+6=7);

3*8=24 (2+4=6);

4*8=32 (3+2=5);

5*8=40 (4+0=4);

6*8=48 (4+8=12, 1+2=3);

7*8=56 (5+6=11, 1+1=2) ...

11264 = 11 * 2^{6+4} .............. [All digits of the number 11264 are used]

2737 = (2 × 7)^3 – 7 ................. [idem]

Royal V. Heath discovered 1118 + 1881 + 8181 + 8818 = 1181 + 1818 + 8118 + 8881

Reverse that and you get:

1888 + 8118 + 8181 + 1811 = 8188 + 1818 + 1881 + 8111

Both equations remain true if you square all their terms.