## 2008年3月28日 星期五

### The Mysterious Fish Number - 153

John 21:11 Simon Peter climbed aboard and dragged the net ashore. It was full of large fish, 153, but even with so many the net was not torn.

The above scripture is taken from the famous bible story "Jesus and the Miraculous Catch of Fish". Having read the scripture, you may wonder why the number of fish was counted and recorded with such a precision. Indeed, scholars throughout history have argued that 153 has a far deeper meaning!

Mathematically, 153 is a wonderful number.

(A) In the binary system, 153 is written as 10011001, which is a symmetric figure.

(B) 153 is a triangular number (1+2+3+...+16+17 = 153).

(C) 153 is the sum of the first 5 factorials (1!+2!+3!+4!+5! = 153).

(D) 153 is the sum of the cube of each of its digits (1^3+5^3+3^3 = 153).

Here comes the grand finale!

(E) Start with any multiple of 3. By repeatedly summing up the cube of each digit, you will always end up with 153 eventually.

Example 1: Take 66.

6^3+6^3 = 432
4^3+3^3+2^3 = 99
9^3+9^3 = 1458
1^3+4^3+5^3+8^3 = 702
7^3+0^3+2^3 = 351
3^3+5^3+1^3 = 153

Example 2: Take 2001.

2^3+0^3+0^3+1^3 = 9
9^3 = 729
7^3+2^3+9^3 = 1080
1^3+0^3+8^3+0^3 = 513
5^3+1^3+3^3 = 153

Do you know why?

#### 2 則留言:

Pop 提到...

1+6+7+17+18+23 = 2+3+11+13+21+22

1^r+6^r+7^r+17^r+18^r+23^r = 2^r+3^r+11^r+13^r+21^r+22^r

for r = 2, 3, 4, 5

whsvin 提到...