#math trivia for #April11: #102 contains three consecutive digits. How many other numbers 100-366 have this property?
— Burt Kaliski Jr. (@modulomathy) April 12, 2012
The simplest way is probably to look at the eight different possible sets of digits involved:
- 0,1,2: 102, 120, 201, 210 (4 ways)
- 1,2,3: 123, 132, 213, 231, 312, 321 (6 ways)
- 2,3,4: 234, 243, 324, 342 (4 ways)
- 3,4,5: 345, 354 (2 ways)
- 4,5,6 through 7,8,9: no ways
A total of 15 other numbers have the same property as 102.
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