Let me provide some facts about a couple of integers m and n:
- One of them is a 3-digit number, the other is a 2-digit number
- One of them is divisible by 11
- One has all its digits distinct
- The last digit of m^3 equals the last digit of n
- The last digit of n^3 equals the last digit of m
a. Evaluate the maximum value of m+n.
b. What possible values can m*n reach?
(In reply to
list continued by Charlie)
There are 632 possible products out of the 1233 pairs of m and n:
1100
2156
2200
2211
2376
2431
2475
2541
2651
2761
2816
2871
2981
3036
3091
3201
3256
3300
3311
3476
3531
3696
3751
3861
3916
3971
4081
4125
4191
4301
4356
4400
4411
4521
4576
4631
4741
4796
4851
4961
5016
5071
5181
5236
5291
5401
5456
5500
5511
5676
5731
5775
5841
5896
5951
6061
6116
6171
6281
6336
6391
6501
6556
6600
6611
6721
6776
6831
6875
6941
6996
7051
7161
7216
7381
7425
7436
7491
7601
7656
7700
7711
7821
7876
7931
7975
8041
8096
8151
8261
8316
8371
8481
8536
8591
8701
8756
8800
8811
8976
9031
9075
9141
9196
9251
9361
9416
9471
9581
9625
9636
9801
9856
9900
9911
10076
10131
10175
10241
10296
10351
10461
10516
10571
10681
10725
10791
10956
11000
11011
11176
11275
11396
11451
11616
11781
11825
11836
11891
12056
12111
12276
12331
12375
12441
12496
12551
12716
12771
12925
12936
13101
13156
13200
13321
13376
13431
13475
13596
13651
13761
13816
13871
13981
14025
14036
14091
14256
14421
14476
14575
14751
14861
14916
15081
15125
15136
15356
15400
15411
15521
15576
15631
15675
15741
15796
16016
16071
16225
16236
16401
16456
16500
16511
16676
16731
16775
16896
16951
17061
17325
17336
17391
17501
17556
17600
17721
17875
18051
18216
18491
18601
18711
18821
18876
18975
19096
19371
19481
19536
19701
19800
19976
20031
20075
20196
20251
20361
20416
20625
20636
20691
20801
20856
21021
21076
21175
21296
21351
21516
21571
21681
21725
21736
21791
22000
22011
22176
22231
22275
22561
22616
22671
22825
22836
23001
23056
23100
23276
23375
23496
23661
23716
23925
23936
24211
24321
24541
24596
24651
24816
25025
25201
25256
25311
25476
25575
25641
25696
25916
26125
26136
26400
26411
26576
26631
26675
26796
26961
27016
27225
27291
27401
27456
27500
27511
27621
27676
27896
27951
28116
28281
28336
28391
28611
28776
28875
29601
29656
29700
29711
29931
30096
30261
30536
30591
30800
30921
30976
31031
31251
31416
31581
31691
31801
31856
31911
32021
32076
32175
32296
32571
32725
32736
33000
33176
33231
33275
33396
33616
33781
33825
33891
34056
34221
34276
34375
34496
34551
34716
34881
34925
34936
35156
35200
35211
35376
35475
35541
35651
35816
36036
36256
36421
36531
36575
36696
37125
37191
37521
37576
37675
37741
37851
37961
38016
38181
38225
38291
38456
38500
38511
38676
38731
38775
38896
39061
39325
39336
39501
39556
39600
39776
39831
39875
40216
40271
40425
40491
40656
40931
40975
41041
41096
41151
41481
41536
41811
41976
42075
42416
42471
42581
42856
42911
43175
43296
43351
43461
43516
43725
43956
44000
44121
44176
44275
44616
44781
44825
44891
45056
45276
45375
45441
45496
45661
45771
45881
45925
45936
46200
46376
46431
46475
46596
46816
47025
47201
47256
47421
47575
47641
47696
47916
47971
48081
48125
48411
48576
49225
49236
49456
49500
49511
49775
49896
50281
50325
50336
50391
50721
50875
51051
51216
51271
51381
51425
51821
51876
51975
52041
52096
52316
52371
52536
52591
52800
52976
53075
53196
53361
53625
53801
53856
53900
54131
54175
54351
54516
54901
55176
55451
55616
55671
55836
56056
56331
56496
56551
57211
57321
57376
57475
57761
57816
57981
58311
58696
58751
59136
59400
59796
59961
60016
60236
60291
60456
60775
60896
61061
61116
61171
61281
61336
61600
61776
61831
61875
62271
62436
62601
62656
63096
63261
63371
63536
64251
64416
64911
65076
65241
65296
65681
66176
66451
66836
67056
67221
67551
67925
68211
68376
68541
68651
68761
68816
69300
69531
69696
69861
70125
70191
70301
70356
70400
70576
71071
71181
71456
71896
72171
72611
73161
73216
73381
74096
74151
74921
74976
75141
75691
75856
76131
76516
76736
77341
77616
77891
78111
78375
78496
78771
78936
79200
79376
79431
79475
80091
80256
81081
81356
82016
82071
82896
83061
83776
84051
84656
85041
85536
86031
86416
86856
87021
87131
88396
88561
88825
89001
89056
89100
90816
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Posted by Charlie
on 2016-11-16 10:19:56 |
part b in more concise form
