Find the smallest distinct whole numbers, M and N such that you can rearrange the digits of M to get N, you can rearrange the digits of M2 to get N2, you can rearrange the digits of M3 to get N3, and where M does not contain the digit zero.
(M,N): 495839, 539894
(M^2,N^2): 245856313921, 291485531236
(M^3,N^3): 121905148838274719, 157371289401128984
The cubes contain a zero but M and N do not.
The first output from the program below was:
M and N are among: [495839, 539894, 598529, 612581, 944441, 965891, 966161]
The squares are among: [245856313921, 291485531236, 358236963841, 375255481561, 891968802481, 932945423881, 933467077921]
The cubes are among: [121905148838274719, 157371289401128984, 214415211730789889, 229874378150118941, 842411907783958121, 901123588417842971, 901879485471231281]
The program was designed to find cubes which share the same digits, but the squares and first powers do not necessarily share the same digits.
In this case, the first two of the each list do share the same digits.
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big = 1000000
numbDict = {}
squareDict = {}
cubeDict = {}
for k in range(1,big):
kSquared = k**2
kCubed = k**3
numbKey = ''.join(sorted(str(k)))
if '0' in numbKey:
continue
squareKey = ''.join(sorted(str(kSquared)))
cubeKey = ''.join(sorted(str(kCubed)))
if numbKey not in numbDict:
numbDict[numbKey] = [k]
else:
numbDict[numbKey].append(k)
if squareKey not in squareDict:
squareDict[squareKey] = [kSquared]
else:
squareDict[squareKey].append(kSquared)
if cubeKey not in cubeDict:
cubeDict[cubeKey] = [kCubed]
else:
cubeDict[cubeKey].append(kCubed)
for k,v in cubeDict.items():
if len(v) == 1:
continue
these_N_keys = []
these_Nsqrd_keys = []
thesenumbs = []
thesesquares = []
for cub in v:
n = round(cub**(1/3))
nsqrd = n**2
keyOfN = ''.join(sorted(str(n)))
keyOfNsqrd = ''.join(sorted(str(nsqrd)))
these_N_keys.append(keyOfN)
these_Nsqrd_keys.append(keyOfNsqrd)
thesenumbs.append(n)
thesesquares.append(n**2)
if len(these_N_keys) == len(set(these_N_keys)):
continue
if len(these_Nsqrd_keys) == len(set(these_Nsqrd_keys)):
continue
print('M and N are among:', thesenumbs )
print('The squares are among:', thesesquares)
print('The cubes are among:', v)
print()
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Posted by Larry
on 2024-03-24 11:58:22 |
Computer solution
