# Taxicab numbers

```ruby
var (start=1, end=25) = ARGV.map{.to_i}...
 
func display (h, start, end) {
    var i = start
    for n in [h.grep {|_,v| v.len > 1 }.keys.sort_by{.to_i}[start-1 .. end-1]] {
        printf("%4d %10d  =>\t%s\n", i++, n,
            h{n}.map{ "%4d³ + %-s" % (.first, "#{.last}³") }.join(",\t"))
    }
}
 
var taxi = Hash()
var taxis = 0
var terminate = 0
 
for c1 (1..Inf) {
    if (0<terminate && terminate<c1) {
        display(taxi, start, end)
        break
    }
    var c = c1**3
    for c2 (1..c1) {
        var this = (c2**3 + c)
        taxi{this} := [] << [c2, c1]
        ++taxis if (taxi{this}.len == 2)
        if (taxis==end && !terminate) {
            terminate = taxi.grep{|_,v| v.len > 1 }.keys.map{.to_i}.max.root(3)
        }
    }
}
```

#### Output:

```
   1       1729  =>        9³ + 10³,       1³ + 12³
   2       4104  =>        9³ + 15³,       2³ + 16³
   3      13832  =>       18³ + 20³,       2³ + 24³
   4      20683  =>       19³ + 24³,      10³ + 27³
   5      32832  =>       18³ + 30³,       4³ + 32³
   6      39312  =>       15³ + 33³,       2³ + 34³
   7      40033  =>       16³ + 33³,       9³ + 34³
   8      46683  =>       27³ + 30³,       3³ + 36³
   9      64232  =>       26³ + 36³,      17³ + 39³
  10      65728  =>       31³ + 33³,      12³ + 40³
  11     110656  =>       36³ + 40³,       4³ + 48³
  12     110808  =>       27³ + 45³,       6³ + 48³
  13     134379  =>       38³ + 43³,      12³ + 51³
  14     149389  =>       29³ + 50³,       8³ + 53³
  15     165464  =>       38³ + 48³,      20³ + 54³
  16     171288  =>       24³ + 54³,      17³ + 55³
  17     195841  =>       22³ + 57³,       9³ + 58³
  18     216027  =>       22³ + 59³,       3³ + 60³
  19     216125  =>       45³ + 50³,       5³ + 60³
  20     262656  =>       36³ + 60³,       8³ + 64³
  21     314496  =>       30³ + 66³,       4³ + 68³
  22     320264  =>       32³ + 66³,      18³ + 68³
  23     327763  =>       51³ + 58³,      30³ + 67³
  24     373464  =>       54³ + 60³,       6³ + 72³
  25     402597  =>       56³ + 61³,      42³ + 69³
```

With passed parameters 2000 and 2006:

#### Output:

```
2000 1671816384  =>      940³ + 944³,    428³ + 1168³
2001 1672470592  =>      632³ + 1124³,    29³ + 1187³
2002 1673170856  =>      828³ + 1034³,   458³ + 1164³
2003 1675045225  =>      744³ + 1081³,   522³ + 1153³
2004 1675958167  =>      711³ + 1096³,   492³ + 1159³
2005 1676926719  =>      714³ + 1095³,    63³ + 1188³
2006 1677646971  =>      891³ + 990³,     99³ + 1188³
```


---

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