main.go

package main

import (
	"fmt"
	"sort"
	"strings"
)

var (
	ws = []float64 {
		2.5,
		5,
		7.5,
		10,
	}
	totals = map[float64][][]float64{}
)

func main() {
	for weights := 1; weights < 6; weights++ {
		f(make([]float64, 0, weights), 0)
	}
	l := []float64{}
	for v := range totals {
		skip := false
		for _, v2 := range ws {
			if v == v2 {
				skip = true
			}
		}
		if skip {
			continue
		}
		l = append(l, v)
	}
	sort.Sort(sort.Reverse(sort.Float64Slice(l)))
	for _, e := range l {
		for _, ee := range totals[e] {
			ssa := []string{}
			for _, eee := range ee {
				sss := fmt.Sprintf("%.1f", eee)
				ssa = append(ssa, sss)
			}
			fmt.Printf("%.1f  = 2 x %.1f  = %s\n", e * 2, e, strings.Join(ssa, " + "))
		}
	}
}

func f(s []float64, p int) bool {
	if cap(s) - len(s) <= 0 {
		sum := 0.0
		for _, v := range s {
			sum += v
		}
		totals[sum] = append(totals[sum], s)
		return true
	}
	for i, w := range ws[p:] {
		r := make([]float64, len(s), cap(s))
		copy(r, s)
		r = append(r, w)
		if !f(r, i+p+1) {
			r = append(r, w)
			f(r, i+p+1)
		}
	}
	return false
}