### BARS::290 Miles From Grand Canyon in Alpine, Arizona

This road sign is along westbound US Hwy-180 near Alpine, Arizona.

The road sign says...

```   +-----------------------+
| Petrified Forest  104 |
| Grand Canyon      290 |
+-----------------------+
```

This road sign was turned in a BARS after we created the `split_into_squares_sum(n)` function during late-April of 2008. The function is used to split a number `n` into a set of square numbers. Each square number in the set must be greater than or equal to four and the numbers in the set must sum to `n`.

```   the numbers are:  104  290

split_into_squares_sum(104) = { 100, 4 }
split_into_squares_sum(290) = { 256, 25, 9 }

the numbers become:  100  4  256  25  9    [the math is:  see (1)]
apply square-roots:   10  2   16   5  3    [the math is:  see (2)]
apply square-roots:   10  2    4   5  3    [the math is:  see (3)]
apply square-roots:   10  2    2   5  3    [the math is:  see (4)]

the math is:
(1)  256 - (4 * 9) - 100 = sqrt(25)!
(2)  16 * 3 + 2 = 5 * 10
(3)  10 + 2 = 3 + 4 + 5
(4)  5! / 10 = 2 * 2 * 3

[let n = 5! and solve for n]  n / 10 = 2 * 2 * 3
```

This is BARS #412 and it was the first BARS to use the `split_into_squares_sum(n)` exclusively for the math.

Creator: Gerald Thurman [gthurman@gmail.com]
Created: 29 April 2008 