Salve a tutti, io avrei una soluzione algoritmica.
Pur non avendo trovato la formula che risponde al tuo quesito, con quest'approccio di forza bruta è possibile determinare - in tempo esponenziale rispetto l'input - la cardinalità dell'insieme delle soluzioni.
Intanto notiamo che n, pur se non esplicitamente richiesto come intero positivo, può essere il risultato della somma di tre interi non negativi sse è un intero non negativo, quindi restituiamo 0 nel caso in cui n sia decimale o negativo;
dopodiché parte la catena:
- per ogni n>0 esiste sempre la soluzione (n+0+0);
- per ogni n>1 esiste (n-1,1,0);
- per ogni n>2 esiste (n-2, 1, 1),(n-2,2,0);
- e così via..
Dopo aver testato tutte le combinazioni, eliminiamo le soluzioni equivalenti e contiamo quelle rimaste.
Ecco una possibile implementazione:
Testo nascosto, fai click qui per vederlo
- Codice:
#!/usr/bin/python
import sys
import os
DEBUG = 0
class Terna:
terna = {}
def __init__(self, n1,n2,n3):
try:
values = [int(n1),int(n2),int(n3)]
values.sort()
if DEBUG > 0: print(str(values))
values_dict = {}
for i in xrange(0,3):
value = values[i]
if(not value in values_dict):
times = values.count(value)
values_dict[value] = times
self.terna = values_dict
except:
print("Error: worng Terna constructor!")
def equivalente(self, AltraTerna):
res = True
for val in self.terna:
try:
if self.terna[val] != AltraTerna.terna[val]:
res = False
except:
res = False
return res
class TreNumeri:
def __init__(self, number):
if(number==0):
print("Storing n=0!")
self.n = int(number)
self.getPermutations()
def getPermutations(self):
n = self.n
collection = [ ] #str(n)+"+0+0"
for x in xrange(0,n):
collection.append( (str(n-x)+"+"+str(x)+"+0") )
if DEBUG>0: print("x:"+str(x)+", y:0, appending:"+str()+(str(n-x)+"+"+str(x)+"+0"))
for y in xrange(1,x):
collection.append( str(n-x)+"+"+str(x-y)+"+"+str(y) )
if DEBUG>0: print("x:"+str(x)+", y:"+str(y)+", appending:"+( str(n-x)+"+"+str(x-y)+"+"+str(y) ))
if DEBUG>0: print(str(collection))
# Removing double solutions:
for coll in collection:
if DEBUG>0: print("\n- Evaluating "+coll+" doubles:")
values = coll.split("+",3)
values_dict = {} # value:occurences
for i in xrange(0,3):
value = values[i]
if(not value in values_dict):
times = values.count(value)
values_dict[value] = times
for coll2 in collection:
if DEBUG>0: print("-"+coll+"- is "+coll+" the same of "+coll2+"?")
if coll2 != coll:
if DEBUG>0: print("-"+coll+"- not exactly... let's find out if he has got the same digits...")
values2 = coll2.split("+",3)
values_dict2 = {} # value:occurences
for i in xrange(0,3):
value = values2[i]
if(not value in values_dict2):
times = values2.count(value)
values_dict2[value] = times
if DEBUG>0: print("-"+coll+"-is "+str(values_dict)+"=="+str(values_dict2)+"?")
are_equivalents = Terna(values[0],values[1],values[2]).equivalente(Terna(values2[0],values2[1],values2[2]))
if(are_equivalents):
if DEBUG>0: print("-"+coll+"- "+str(coll)+" is equal to "+str(coll2)+".. Removing the second!\n")
collection.pop(collection.index(coll2))
print("We've got "+str(len(collection))+" results:")
print(str(collection))
argLen = len(sys.argv)
if(argLen<2 ):
print("Error: excepting a second argument!")
exit()
try:
int(sys.argv[1])
except:
if(float(sys.argv[1])):
print("The result is 0.")
else:
print("Error: excepting a numbeer!")
exit()
if(argLen>2): DEBUG = 1
res = TreNumeri(int(sys.argv[1]))
Scusate se è disordinato e poco elegante ma è fatto di fretta!
Ecco alcuni output d'esempio:
Testo nascosto, fai click qui per vederlo
python ./tre_numeri.py 4
We've got 4 results:
['4+0+0', '3+1+0', '2+2+0', '1+1+2']
python ./tre_numeri.py 5
We've got 5 results:
['5+0+0', '4+1+0', '3+2+0', '3+1+1', '1+2+2']
python ./tre_numeri.py 6
We've got 7 results:
['6+0+0', '5+1+0', '4+2+0', '4+1+1', '3+3+0', '2+3+1', '2+2+2']
python ./tre_numeri.py 7
We've got 9 results:
['7+0+0', '6+1+0', '5+2+0', '5+1+1', '4+3+0', '4+2+1', '3+3+1', '2+2+3', '1+4+2']
python ./tre_numeri.py 8
We've got 11 results:
['8+0+0', '7+1+0', '6+2+0', '6+1+1', '5+3+0', '5+2+1', '4+4+0', '4+2+2', '3+4+1', '3+2+3', '1+5+2']
python ./tre_numeri.py 9
We've got 12 results:
['9+0+0', '8+1+0', '7+2+0', '7+1+1', '6+3+0', '5+4+0', '5+3+1', '5+2+2', '4+4+1', '3+4+2', '3+3+3', '1+6+2']
python ./tre_numeri.py 10
We've got 16 results:
['10+0+0', '9+1+0', '8+2+0', '8+1+1', '7+3+0', '7+2+1', '6+4+0', '6+3+1', '6+2+2', '5+5+0', '4+5+1', '4+3+3', '4+2+4', '3+3+4', '2+5+3', '1+7+2']
python ./tre_numeri.py 11
We've got 17 results:
['11+0+0', '10+1+0', '9+2+0', '9+1+1', '8+3+0', '7+4+0', '7+3+1', '7+2+2', '6+5+0', '6+4+1', '6+3+2', '5+5+1', '5+3+3', '4+5+2', '4+3+4', '2+6+3', '1+8+2']
python ./tre_numeri.py 12
We've got 20 results:
['12+0+0', '11+1+0', '10+2+0', '10+1+1', '9+3+0', '8+4+0', '8+3+1', '8+2+2', '7+5+0', '7+4+1', '7+3+2', '6+6+0', '6+4+2', '6+3+3', '5+6+1', '5+2+5', '4+4+4', '3+5+4', '2+7+3', '1+9+2']
python ./tre_numeri.py 13
We've got 23 results:
['13+0+0', '12+1+0', '11+2+0', '11+1+1', '10+3+0', '9+4+0', '9+3+1', '9+2+2', '8+5+0', '8+4+1', '8+3+2', '7+6+0', '7+5+1', '7+4+2', '7+3+3', '6+6+1', '5+6+2', '5+4+4', '5+3+5', '4+4+5', '3+6+4', '2+8+3', '1+10+2']
python ./tre_numeri.py 13
We've got 23 results:
['13+0+0', '12+1+0', '11+2+0', '11+1+1', '10+3+0', '9+4+0', '9+3+1', '9+2+2', '8+5+0', '8+4+1', '8+3+2', '7+6+0', '7+5+1', '7+4+2', '7+3+3', '6+6+1', '5+6+2', '5+4+4', '5+3+5', '4+4+5', '3+6+4', '2+8+3', '1+10+2']
python ./tre_numeri.py 14
We've got 26 results:
['14+0+0', '13+1+0', '12+2+0', '12+1+1', '11+3+0', '10+4+0', '10+3+1', '10+2+2', '9+5+0', '9+4+1', '9+3+2', '8+6+0', '8+5+1', '8+4+2', '8+3+3', '7+7+0', '7+5+2', '7+4+3', '6+7+1', '6+4+4', '6+2+6', '5+4+5', '3+7+4', '3+5+6', '2+9+3', '1+11+2']
python ./tre_numeri.py 15
We've got 29 results:
['15+0+0', '14+1+0', '13+2+0', '13+1+1', '12+3+0', '12+2+1', '11+4+0', '11+3+1', '11+2+2', '10+5+0', '10+4+1', '9+6+0', '9+5+1', '9+4+2', '9+3+3', '8+7+0', '8+6+1', '8+5+2', '8+4+3', '7+7+1', '7+5+3', '7+4+4', '6+7+2', '6+3+6', '5+5+5', '4+6+5', '3+8+4', '2+10+3', '1+12+2']
python ./tre_numeri.py 16
We've got 33 results:
['16+0+0', '15+1+0', '14+2+0', '14+1+1', '13+3+0', '12+4+0', '12+3+1', '12+2+2', '11+5+0', '11+4+1', '11+3+2', '10+6+0', '10+5+1', '10+4+2', '10+3+3', '9+7+0', '9+6+1', '9+5+2', '9+4+3', '8+8+0', '8+6+2', '8+5+3', '8+4+4', '7+8+1', '7+2+7', '6+5+5', '6+4+6', '5+5+6', '4+7+5', '3+9+4', '3+6+7', '2+11+3', '1+13+2']
python ./tre_numeri.py 17
We've got 36 results:
['17+0+0', '16+1+0', '15+2+0', '15+1+1', '14+3+0', '14+2+1', '13+4+0', '13+3+1', '13+2+2', '12+5+0', '12+4+1', '11+6+0', '11+5+1', '11+4+2', '11+3+3', '10+7+0', '10+6+1', '10+5+2', '10+4+3', '9+8+0', '9+7+1', '9+6+2', '9+5+3', '9+4+4', '8+8+1', '8+6+3', '8+5+4', '7+8+2', '7+5+5', '7+3+7', '6+5+6', '4+8+5', '4+6+7', '3+10+4', '2+12+3', '1+14+2']
python ./tre_numeri.py 18
We've got 40 results:
['18+0+0', '17+1+0', '16+2+0', '16+1+1', '15+3+0', '15+2+1', '14+4+0', '14+3+1', '14+2+2', '13+5+0', '13+4+1', '12+6+0', '12+5+1', '12+4+2', '12+3+3', '11+7+0', '11+6+1', '11+5+2', '10+8+0', '10+7+1', '10+6+2', '10+5+3', '10+4+4', '9+9+0', '9+7+2', '9+6+3', '9+5+4', '8+9+1', '8+7+3', '8+6+4', '8+5+5', '8+2+8', '7+4+7', '6+6+6', '5+7+6', '4+9+5', '3+11+4', '3+7+8', '2+13+3', '1+15+2']
python ./tre_numeri.py 180
We've got 2834 results:
['180+0+0', '179+1+0', '178+2+0', '178+1+1', '177+3+0', '176+4+0', '176+3+1', '176+2+2', '175+5+0', '175+4+1', '175+3+2', '174+6+0', '174+5+1', '174+4+2', '174+3+3', '173+7+0', '173+6+1', '173+5+2', '173+4+3', '172+8+0', '172+7+1', '172+6+2', '172+5+3', '172+4+4', '171+9+0', '171+8+1', '171+7+2', '171+6+3', '170+10+0', '170+9+1', '170+8+2', '170+7+3', '170+6+4', '170+5+5', '169+11+0', '169+10+1', '169+9+2', '169+8+3', '169+7+4', '168+12+0', '168+11+1', '168+10+2', '168+9+3', '168+8+4', '168+7+5', '168+6+6', '167+13+0', '167+12+1', '167+11+2', '167+10+3', '167+9+4', '167+8+5', '167+7+6', '166+14+0', '166+13+1', '166+12+2', '166+11+3', '166+10+4', '166+9+5', '166+8+6', '166+7+7', '165+15+0', '165+14+1', '165+13+2', '165+12+3', '165+11+4', '165+10+5', '165+9+6', '165+8+7', '164+16+0', '164+15+1', '164+14+2', '164+13+3', '164+12+4', '164+11+5', '164+10+6', '164+9+7', '164+8+8', '163+17+0', '163+16+1', '163+15+2', '163+14+3', '163+13+4', '163+12+5', '163+11+6', '163+10+7', '162+18+0', '162+17+1', '162+16+2', '162+15+3', '162+14+4', '162+13+5', '162+12+6', '162+11+7', '162+10+8', '162+9+9', '161+19+0', '161+18+1', '161+17+2', '161+16+3', '161+15+4', '161+14+5', '161+13+6', '161+12+7', '161+11+8', '160+20+0', '160+19+1', '160+18+2', '160+17+3', '160+16+4', '160+15+5', '160+14+6', '160+13+7', '160+12+8', '160+11+9', '160+10+10', '159+21+0', '159+20+1', '159+19+2', '159+18+3', '159+17+4', '159+16+5', '159+15+6', '159+14+7', '159+13+8', '159+12+9', '159+11+10', '158+22+0', '158+21+1', '158+20+2', '158+19+3', '158+18+4', '158+17+5', '158+16+6', '158+15+7', '158+14+8', '158+13+9', '158+12+10', '158+11+11', '157+23+0', '157+22+1', '157+21+2', '157+20+3', '157+19+4', '157+18+5', '157+17+6', '157+16+7', '157+15+8', '157+14+9', '157+13+10', '157+12+11', '156+24+0', '156+23+1', '156+22+2', '156+21+3', '156+20+4', '156+19+5', '156+18+6', '156+17+7', '156+16+8', '156+15+9', '156+14+10', '156+13+11', '156+12+12', '155+25+0', '155+24+1', '155+23+2', '155+22+3', '155+21+4', '155+20+5', '155+19+6', '155+18+7', '155+17+8', '155+16+9', '155+15+10', '155+14+11', '154+26+0', '154+25+1', '154+24+2', '154+23+3', '154+22+4', '154+21+5', '154+20+6', '154+19+7', '154+18+8', '154+17+9', '154+16+10', '154+15+11', '154+14+12', '154+13+13', '153+27+0', '153+26+1', '153+25+2', '153+24+3', '153+23+4', '153+22+5', '153+21+6', '153+20+7', '153+19+8', '153+18+9', '153+17+10', '153+16+11', '153+15+12', '152+28+0', '152+27+1', '152+26+2', '152+25+3', '152+24+4', '152+23+5', '152+22+6', '152+21+7', '152+20+8', '152+19+9', '152+18+10', '152+17+11', '152+16+12', '152+15+13', '152+14+14', '151+29+0', '151+28+1', '151+27+2', '151+26+3', '151+25+4', '151+24+5', '151+23+6', '151+22+7', '151+21+8', '151+20+9', '151+19+10', '151+18+11', '151+17+12', '151+16+13', '151+15+14', '150+30+0', '150+29+1', '150+28+2', '150+27+3', '150+26+4', '150+25+5', '150+24+6', '150+23+7', '150+22+8', '150+21+9', '150+20+10', '150+19+11', '150+18+12', '150+17+13', '150+16+14', '150+15+15', '149+31+0', '149+30+1', '149+29+2', '149+28+3', '149+27+4', '149+26+5', '149+25+6', '149+24+7', '149+23+8', '149+22+9', '149+21+10', '149+20+11', '149+19+12', '149+18+13', '149+17+14', '149+16+15', '148+32+0', '148+31+1', '148+30+2', '148+29+3', '148+28+4', '148+27+5', '148+26+6', '148+25+7', '148+24+8', '148+23+9', '148+22+10', '148+21+11', '148+20+12', '148+19+13', '148+18+14', '148+17+15', '148+16+16', '147+33+0', '147+32+1', '147+31+2', '147+30+3', '147+29+4', '147+28+5', '147+27+6', '147+26+7', '147+25+8', '147+24+9', '147+23+10', '147+22+11', '147+21+12', '147+20+13', '147+19+14', '147+18+15', '146+34+0', '146+33+1', '146+32+2', '146+31+3', '146+30+4', '146+29+5', '146+28+6', '146+27+7', '146+26+8', '146+25+9', '146+24+10', '146+23+11', '146+22+12', '146+21+13', '146+20+14', '146+19+15', '146+18+16', '146+17+17', '145+35+0', '145+34+1', '145+33+2', '145+32+3', '145+31+4', '145+30+5', '145+29+6', '145+28+7', '145+27+8', '145+26+9', '145+25+10', '145+24+11', '145+23+12', '145+22+13', '145+21+14', '145+20+15', '145+19+16', '144+36+0', '144+35+1', '144+34+2', '144+33+3', '144+32+4', '144+31+5', '144+30+6', '144+29+7', '144+28+8', '144+27+9', '144+26+10', '144+25+11', '144+24+12', '144+23+13', '144+22+14', '144+21+15', '144+20+16', '144+19+17', '144+18+18', '143+37+0', '143+36+1', '143+35+2', '143+34+3', '143+33+4', '143+32+5', '143+31+6', '143+30+7', '143+29+8', '143+28+9', '143+27+10', '143+26+11', '143+25+12', '143+24+13', '143+23+14', '143+22+15', '143+21+16', '143+20+17', '143+19+18', '142+38+0', '142+37+1', '142+36+2', '142+35+3', '142+34+4', '142+33+5', '142+32+6', '142+31+7', '142+30+8', '142+29+9', '142+28+10', '142+27+11', '142+26+12', '142+25+13', '142+24+14', '142+23+15', '142+22+16', '142+21+17', '142+20+18', '142+19+19', '141+39+0', '141+38+1', '141+37+2', '141+36+3', '141+35+4', '141+34+5', '141+33+6', '141+32+7', '141+31+8', '141+30+9', '141+29+10', '141+28+11', '141+27+12', '141+26+13', '141+25+14', '141+24+15', '141+23+16', '141+22+17', '141+21+18', '141+20+19', '140+40+0', '140+39+1', '140+38+2', '140+37+3', '140+36+4', '140+35+5', '140+34+6', '140+33+7', '140+32+8', '140+31+9', '140+30+10', '140+29+11', '140+28+12', '140+27+13', '140+26+14', '140+25+15', '140+24+16', '140+23+17', '140+22+18', '140+21+19', '140+20+20', '139+41+0', '139+40+1', '139+39+2', '139+38+3', '139+37+4', '139+36+5', '139+35+6', '139+34+7', '139+33+8', '139+32+9', '139+31+10', '139+30+11', '139+29+12', '139+28+13', '139+27+14', '139+26+15', '139+25+16', '139+24+17', '139+23+18', '139+22+19', '138+42+0', '138+41+1', '138+40+2', '138+39+3', '138+38+4', '138+37+5', '138+36+6', '138+35+7', '138+34+8', '138+33+9', '138+32+10', '138+31+11', '138+30+12', '138+29+13', '138+28+14', '138+27+15', '138+26+16', '138+25+17', '138+24+18', '138+23+19', '138+22+20', '138+21+21', '137+43+0', '137+42+1', '137+41+2', '137+40+3', '137+39+4', '137+38+5', '137+37+6', '137+36+7', '137+35+8', '137+34+9', '137+33+10', '137+32+11', '137+31+12', '137+30+13', '137+29+14', '137+28+15', '137+27+16', '137+26+17', '137+25+18', '137+24+19', '137+23+20', '136+44+0', '136+43+1', '136+42+2', '136+41+3', '136+40+4', '136+39+5', '136+38+6', '136+37+7', '136+36+8', '136+35+9', '136+34+10', '136+33+11', '136+32+12', '136+31+13', '136+30+14', '136+29+15', '136+28+16', '136+27+17', '136+26+18', '136+25+19', '136+24+20', '136+23+21', '136+22+22', '135+45+0', '135+44+1', '135+43+2', '135+42+3', '135+41+4', '135+40+5', '135+39+6', '135+38+7', '135+37+8', '135+36+9', '135+35+10', '135+34+11', '135+33+12', '135+32+13', '135+31+14', '135+30+15', '135+29+16', '135+28+17', '135+27+18', '135+26+19', '135+25+20', '135+24+21', '135+23+22', '134+46+0', '134+45+1', '134+44+2', '134+43+3', '134+42+4', '134+41+5', '134+40+6', '134+39+7', '134+38+8', '134+37+9', '134+36+10', '134+35+11', '134+34+12', '134+33+13', '134+32+14', '134+31+15', '134+30+16', '134+29+17', '134+28+18', '134+27+19', '134+26+20', '134+25+21', '134+24+22', '134+23+23', '133+47+0', '133+46+1', '133+45+2', '133+44+3', '133+43+4', '133+42+5', '133+41+6', '133+40+7', '133+39+8', '133+38+9', '133+37+10', '133+36+11', '133+35+12', '133+34+13', '133+33+14', '133+32+15', '133+31+16', '133+30+17', '133+29+18', '133+28+19', '133+27+20', '133+26+21', '133+25+22', '133+24+23', '132+48+0', '132+47+1', '132+46+2', '132+45+3', '132+44+4', '132+43+5', '132+42+6', '132+41+7', '132+40+8', '132+39+9', '132+38+10', '132+37+11', '132+36+12', '132+35+13', '132+34+14', '132+33+15', '132+32+16', '132+31+17', '132+30+18', '132+29+19', '132+28+20', '132+27+21', '132+26+22', '132+25+23', '132+24+24', '131+49+0', '131+48+1', '131+47+2', '131+46+3', '131+45+4', '131+44+5', '131+43+6', '131+42+7', '131+41+8', '131+40+9', '131+39+10', '131+38+11', '131+37+12', '131+36+13', '131+35+14', '131+34+15', '131+33+16', '131+32+17', '131+31+18', '131+30+19', '131+29+20', '131+28+21', '131+27+22', '131+26+23', '130+50+0', '130+49+1', '130+48+2', '130+47+3', '130+46+4', '130+45+5', '130+44+6', '130+43+7', '130+42+8', '130+41+9', '130+40+10', '130+39+11', '130+38+12', '130+37+13', '130+36+14', '130+35+15', '130+34+16', '130+33+17', '130+32+18', '130+31+19', '130+30+20', '130+29+21', '130+28+22', '130+27+23', '130+26+24', '130+25+25', '129+51+0', '129+50+1', '129+49+2', '129+48+3', '129+47+4', '129+46+5', '129+45+6', '129+44+7', '129+43+8', '129+42+9', '129+41+10', '129+40+11', '129+39+12', '129+38+13', '129+37+14', '129+36+15', '129+35+16', '129+34+17', '129+33+18', '129+32+19', '129+31+20', '129+30+21', '129+29+22', '129+28+23', '129+27+24', '128+52+0', '128+51+1', '128+50+2', '128+49+3', '128+48+4', '128+47+5', '128+46+6', '128+45+7', '128+44+8', '128+43+9', '128+42+10', '128+41+11', '128+40+12', '128+39+13', '128+38+14', '128+37+15', '128+36+16', '128+35+17', '128+34+18', '128+33+19', '128+32+20', '128+31+21', '128+30+22', '128+29+23', '128+28+24', '128+27+25', '128+26+26', '127+53+0', '127+52+1', '127+51+2', '127+50+3', '127+49+4', '127+48+5', '127+47+6', '127+46+7', '127+45+8', '127+44+9', '127+43+10', '127+42+11', '127+41+12', '127+40+13', '127+39+14', '127+38+15', '127+37+16', '127+36+17', '127+35+18', '127+34+19', '127+33+20', '127+32+21', '127+31+22', '127+30+23', '127+29+24', '127+28+25', '127+27+26', '126+54+0', '126+53+1', '126+52+2', '126+51+3', '126+50+4', '126+49+5', '126+48+6', '126+47+7', '126+46+8', '126+45+9', '126+44+10', '126+43+11', '126+42+12', '126+41+13', '126+40+14', '126+39+15', '126+38+16', '126+37+17', '126+36+18', '126+35+19', '126+34+20', '126+33+21', '126+32+22', '126+31+23', '126+30+24', '126+29+25', '126+28+26', '126+27+27', '125+55+0', '125+54+1', '125+53+2', '125+52+3', '125+51+4', '125+50+5', '125+49+6', '125+48+7', '125+47+8', '125+46+9', '125+45+10', '125+44+11', '125+43+12', '125+42+13', '125+41+14', '125+40+15', '125+39+16', '125+38+17', '125+37+18', '125+36+19', '125+35+20', '125+34+21', '125+33+22', '125+32+23', '125+31+24', '125+30+25', '125+29+26', '125+28+27', '124+56+0', '124+55+1', '124+54+2', '124+53+3', '124+52+4', '124+51+5', '124+50+6', '124+49+7', '124+48+8', '124+47+9', '124+46+10', '124+45+11', '124+44+12', '124+43+13', '124+42+14', '124+41+15', '124+40+16', '124+39+17', '124+38+18', '124+37+19', '124+36+20', '124+35+21', '124+34+22', '124+33+23', '124+32+24', '124+31+25', '124+30+26', '124+29+27', '124+28+28', '123+57+0', '123+56+1', '123+55+2', '123+54+3', '123+53+4', '123+52+5', '123+51+6', '123+50+7', '123+49+8', '123+48+9', '123+47+10', '123+46+11', '123+45+12', '123+44+13', '123+43+14', '123+42+15', '123+41+16', '123+40+17', '123+39+18', '123+38+19', '123+37+20', '123+36+21', '123+35+22', '123+34+23', '123+33+24', '123+32+25', '123+31+26', '123+30+27', '122+58+0', '122+57+1', '122+56+2', '122+55+3', '122+54+4', '122+53+5', '122+52+6', '122+51+7', '122+50+8', '122+49+9', '122+48+10', '122+47+11', '122+46+12', '122+45+13', '122+44+14', '122+43+15', '122+42+16', '122+41+17', '122+40+18', '122+39+19', '122+38+20', '122+37+21', '122+36+22', '122+35+23', '122+34+24', '122+33+25', '122+32+26', '122+31+27', '122+30+28', '122+29+29', '121+59+0', '121+58+1', '121+57+2', '121+56+3', '121+55+4', '121+54+5', '121+53+6', '121+52+7', '121+51+8', '121+50+9', '121+49+10', '121+48+11', '121+47+12', '121+46+13', '121+45+14', '121+44+15', '121+43+16', '121+42+17', '121+41+18', '121+40+19', '121+39+20', '121+38+21', '121+37+22', '121+36+23', '121+35+24', '121+34+25', '121+33+26', '121+32+27', '121+31+28', '120+60+0', '120+59+1', '120+58+2', '120+57+3', '120+56+4', '120+55+5', '120+54+6', '120+53+7', '120+52+8', '120+51+9', '120+50+10', '120+49+11', '120+48+12', '120+47+13', '120+46+14', '120+45+15', '120+44+16', '120+43+17', '120+42+18', '120+41+19', '120+40+20', '120+39+21', '120+38+22', '120+37+23', '120+36+24', '120+35+25', '120+34+26', '120+33+27', '120+32+28', '120+31+29', '120+30+30', '119+61+0', '119+60+1', '119+59+2', '119+58+3', '119+57+4', '119+56+5', '119+55+6', '119+54+7', '119+53+8', '119+52+9', '119+51+10', '119+50+11', '119+49+12', '119+48+13', '119+47+14', '119+46+15', '119+45+16', '119+44+17', '119+43+18', '119+42+19', '119+41+20', '119+40+21', '119+39+22', '119+38+23', '119+37+24', '119+36+25', '119+35+26', '119+34+27', '119+33+28', '119+32+29', '119+31+30', '118+62+0', '118+61+1', '118+60+2', '118+59+3', '118+58+4', '118+57+5', '118+56+6', '118+55+7', '118+54+8', '118+53+9', '118+52+10', '118+51+11', '118+50+12', '118+49+13', '118+48+14', '118+47+15', '118+46+16', '118+45+17', '118+44+18', '118+43+19', '118+42+20', '118+41+21', '118+40+22', '118+39+23', '118+38+24', '118+37+25', '118+36+26', '118+35+27', '118+34+28', '118+33+29', '118+32+30', '118+31+31', '117+63+0', '117+62+1', '117+61+2', '117+60+3', '117+59+4', '117+58+5', '117+57+6', '117+56+7', '117+55+8', '117+54+9', '117+53+10', '117+52+11', '117+51+12', '117+50+13', '117+49+14', '117+48+15', '117+47+16', '117+46+17', '117+45+18', '117+44+19', '117+43+20', '117+42+21', '117+41+22', '117+40+23', '117+39+24', '117+38+25', '117+37+26', '117+36+27', '117+35+28', '117+34+29', '117+33+30', '117+32+31', '116+64+0', '116+63+1', '116+62+2', '116+61+3', '116+60+4', '116+59+5', '116+58+6', '116+57+7', '116+56+8', '116+55+9', '116+54+10', '116+53+11', '116+52+12', '116+51+13', '116+50+14', '116+49+15', '116+48+16', '116+47+17', '116+46+18', '116+45+19', '116+44+20', '116+43+21', '116+42+22', '116+41+23', '116+40+24', '116+39+25', '116+38+26', '116+37+27', '116+36+28', '116+35+29', '116+34+30', '116+33+31', '116+32+32', '115+65+0', '115+64+1', '115+63+2', '115+62+3', '115+61+4', '115+60+5', '115+59+6', '115+58+7', '115+57+8', '115+56+9', '115+55+10', '115+54+11', '115+53+12', '115+52+13', '115+51+14', '115+50+15', '115+49+16', '115+48+17', '115+47+18', '115+46+19', '115+45+20', '115+44+21', '115+43+22', '115+42+23', '115+41+24', '115+40+25', '115+39+26', '115+38+27', '115+37+28', '115+36+29', '115+35+30', '115+34+31', '114+66+0', '114+65+1', '114+64+2', '114+63+3', '114+62+4', '114+61+5', '114+60+6', '114+59+7', '114+58+8', '114+57+9', '114+56+10', '114+55+11', '114+54+12', '114+53+13', '114+52+14', '114+51+15', '114+50+16', '114+49+17', '114+48+18', '114+47+19', '114+46+20', '114+45+21', '114+44+22', '114+43+23', '114+42+24', '114+41+25', '114+40+26', '114+39+27', '114+38+28', '114+37+29', '114+36+30', '114+35+31', '114+34+32', '114+33+33', '113+67+0', '113+66+1', '113+65+2', '113+64+3', '113+63+4', '113+62+5', '113+61+6', '113+60+7', '113+59+8', '113+58+9', '113+57+10', '113+56+11', '113+55+12', '113+54+13', '113+53+14', '113+52+15', '113+51+16', '113+50+17', '113+49+18', '113+48+19', '113+47+20', '113+46+21', '113+45+22', '113+44+23', '113+43+24', '113+42+25', '113+41+26', '113+40+27', '113+39+28', '113+38+29', '113+37+30', '113+36+31', '113+35+32', '112+68+0', '112+67+1', '112+66+2', '112+65+3', '112+64+4', '112+63+5', '112+62+6', '112+61+7', '112+60+8', '112+59+9', '112+58+10', '112+57+11', '112+56+12', '112+55+13', '112+54+14', '112+53+15', '112+52+16', '112+51+17', '112+50+18', '112+49+19', '112+48+20', '112+47+21', '112+46+22', '112+45+23', '112+44+24', '112+43+25', '112+42+26', '112+41+27', '112+40+28', '112+39+29', '112+38+30', '112+37+31', '112+36+32', '112+35+33', '112+34+34', '111+69+0', '111+68+1', '111+67+2', '111+66+3', '111+65+4', '111+64+5', '111+63+6', '111+62+7', '111+61+8', '111+60+9', '111+59+10', '111+58+11', '111+57+12', '111+56+13', '111+55+14', '111+54+15', '111+53+16', '111+52+17', '111+51+18', '111+50+19', '111+49+20', '111+48+21', '111+47+22', '111+46+23', '111+45+24', '111+44+25', '111+43+26', '111+42+27', '111+41+28', '111+40+29', '111+39+30', '111+38+31', '111+37+32', '111+36+33', '111+35+34', '110+70+0', '110+69+1', '110+68+2', '110+67+3', '110+66+4', '110+65+5', '110+64+6', '110+63+7', '110+62+8', '110+61+9', '110+60+10', '110+59+11', '110+58+12', '110+57+13', '110+56+14', '110+55+15', '110+54+16', '110+53+17', '110+52+18', '110+51+19', '110+50+20', '110+49+21', '110+48+22', '110+47+23', '110+46+24', '110+45+25', '110+44+26', '110+43+27', '110+42+28', '110+41+29', '110+40+30', '110+39+31', '110+38+32', '110+37+33', '110+36+34', '110+35+35', '109+71+0', '109+70+1', '109+69+2', '109+68+3', '109+67+4', '109+66+5', '109+65+6', '109+64+7', '109+63+8', '109+62+9', '109+61+10', '109+60+11', '109+59+12', '109+58+13', '109+57+14', '109+56+15', '109+55+16', '109+54+17', '109+53+18', '109+52+19', '109+51+20', '109+50+21', '109+49+22', '109+48+23', '109+47+24', '109+46+25', '109+45+26', '109+44+27', '109+43+28', '109+42+29', '109+41+30', '109+40+31', '109+39+32', '109+38+33', '109+37+34', '109+36+35', '108+72+0', '108+71+1', '108+70+2', '108+69+3', '108+68+4', '108+67+5', '108+66+6', '108+65+7', '108+64+8', '108+63+9', '108+62+10', '108+61+11', '108+60+12', '108+59+13', '108+58+14', '108+57+15', '108+56+16', '108+55+17', '108+54+18', '108+53+19', '108+52+20', '108+51+21', '108+50+22', '108+49+23', '108+48+24', '108+47+25', '108+46+26', '108+45+27', '108+44+28', '108+43+29', '108+42+30', '108+41+31', '108+40+32', '108+39+33', '108+38+34', '108+37+35', '108+36+36', '107+73+0', '107+72+1', 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'78+61+41', '78+60+42', '78+59+43', '78+58+44', '78+57+45', '78+56+46', '78+55+47', '78+54+48', '78+53+49', '78+52+50', '78+51+51', '78+24+78', '77+75+28', '77+74+29', '77+73+30', '77+72+31', '77+71+32', '77+70+33', '77+69+34', '77+68+35', '77+67+36', '77+66+37', '77+65+38', '77+64+39', '77+63+40', '77+62+41', '77+61+42', '77+60+43', '77+59+44', '77+58+45', '77+57+46', '77+56+47', '77+55+48', '77+54+49', '77+53+50', '77+52+51', '77+26+77', '76+75+29', '76+74+30', '76+73+31', '76+72+32', '76+71+33', '76+70+34', '76+69+35', '76+68+36', '76+67+37', '76+66+38', '76+65+39', '76+64+40', '76+63+41', '76+62+42', '76+61+43', '76+60+44', '76+59+45', '76+58+46', '76+57+47', '76+56+48', '76+55+49', '76+54+50', '76+53+51', '76+52+52', '76+28+76', '75+73+32', '75+72+33', '75+71+34', '75+70+35', '75+69+36', '75+68+37', '75+67+38', '75+66+39', '75+65+40', '75+64+41', '75+63+42', '75+62+43', '75+61+44', '75+60+45', '75+59+46', '75+58+47', '75+57+48', '75+56+49', '75+55+50', '75+54+51', '75+30+75', '74+73+33', '74+72+34', '74+71+35', '74+70+36', '74+69+37', '74+68+38', '74+67+39', '74+66+40', '74+65+41', '74+64+42', '74+63+43', '74+62+44', '74+61+45', '74+60+46', '74+59+47', '74+58+48', '74+57+49', '74+56+50', '74+55+51', '74+54+52', '74+53+53', '74+32+74', '73+71+36', '73+70+37', '73+69+38', '73+68+39', '73+67+40', '73+66+41', '73+65+42', '73+64+43', '73+63+44', '73+62+45', '73+61+46', '73+60+47', '73+59+48', '73+58+49', '73+57+50', '73+56+51', '73+55+52', '73+34+73', '72+71+37', '72+70+38', '72+69+39', '72+68+40', '72+67+41', '72+66+42', '72+65+43', '72+64+44', '72+63+45', '72+62+46', '72+61+47', '72+60+48', '72+59+49', '72+58+50', '72+57+51', '72+56+52', '72+55+53', '72+54+54', '72+36+72', '71+69+40', '71+68+41', '71+67+42', '71+66+43', '71+65+44', '71+64+45', '71+63+46', '71+62+47', '71+61+48', '71+60+49', '71+59+50', '71+58+51', '71+57+52', '71+56+53', '71+55+54', '71+38+71', '70+69+41', '70+68+42', '70+67+43', '70+66+44', '70+65+45', '70+64+46', '70+63+47', '70+62+48', '70+61+49', '70+60+50', '70+59+51', '70+58+52', '70+57+53', '70+56+54', '70+55+55', '70+40+70', '69+67+44', '69+66+45', '69+65+46', '69+64+47', '69+63+48', '69+62+49', '69+61+50', '69+60+51', '69+59+52', '69+58+53', '69+57+54', '69+56+55', '69+42+69', '68+67+45', '68+66+46', '68+65+47', '68+64+48', '68+63+49', '68+62+50', '68+61+51', '68+60+52', '68+59+53', '68+58+54', '68+57+55', '68+56+56', '68+44+68', '67+65+48', '67+64+49', '67+63+50', '67+62+51', '67+61+52', '67+60+53', '67+59+54', '67+58+55', '67+46+67', '66+65+49', '66+64+50', '66+63+51', '66+62+52', '66+61+53', '66+60+54', '66+59+55', '66+58+56', '66+57+57', '66+48+66', '65+63+52', '65+62+53', '65+61+54', '65+60+55', '65+59+56', '65+50+65', '64+63+53', '64+62+54', '64+61+55', '64+60+56', '64+59+57', '64+58+58', '64+52+64', '63+61+56', '63+60+57', '63+59+58', '63+54+63', '62+61+57', '62+60+58', '62+59+59', '62+56+62', '61+58+61', '60+60+60', '59+61+60', '58+63+59', '57+65+58', '57+61+62', '56+67+57', '55+69+56', '55+62+63', '54+71+55', '53+73+54', '53+63+64', '52+75+53', '51+77+52', '51+64+65', '50+79+51', '49+81+50', '49+65+66', '48+83+49', '47+85+48', '47+66+67', '46+87+47', '45+89+46', '45+67+68', '44+91+45', '43+93+44', '43+68+69', '42+95+43', '41+97+42', '41+69+70', '40+99+41', '39+101+40', '39+70+71', '38+103+39', '37+105+38', '37+71+72', '36+107+37', '35+109+36', '35+72+73', '34+111+35', '33+113+34', '33+73+74', '32+115+33', '31+117+32', '31+74+75', '30+119+31', '29+121+30', '29+75+76', '28+123+29', '27+125+28', '27+76+77', '26+127+27', '25+129+26', '25+77+78', '24+131+25', '23+133+24', '23+78+79', '22+135+23', '21+137+22', '21+79+80', '20+139+21', '19+141+20', '19+80+81', '18+143+19', '17+145+18', '17+81+82', '16+147+17', '15+149+16', '15+82+83', '14+151+15', '13+153+14', '13+83+84', '12+155+13', '11+157+12', '11+84+85', '10+159+11', '9+161+10', '9+85+86', '8+163+9', '7+165+8', '7+86+87', '6+167+7', '5+169+6', '5+87+88', '4+171+5', '3+173+4', '3+88+89', '2+175+3', '1+177+2']
La soluzione al p.to b può essere ottenuta facilmente a partire da quella del p.to a eliminando dalle soluzioni quelle in cui compare lo zero.
Attendo feedback!
da axpgn » 14/01/2019, 00:20 
ho sbagliato qualcosa nei conti 
intanto ci ragiono ancora 
