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How many distinct positive digit integers can be formed using the digits 1 to 4 each once such that no adjacent digits differ by more then two?
Wiki User
∙ 7y ago
Well, let's see.
The number of distinct ways to order the digits 1 to 4 is 4x3x2(x1) = 24. That's not too many to list, so let's do so:
1234
1243
1324
1342
1423
1432
2134
2143
2314
2341
2413
2431
3124
3142
3214
3241
3412
3421
4123
4132
4213
4231
4312
4321
The ones where 1 and 4 are next to each other are forbidden by your adjacent numbers rule. That's 2 of the numbers starting with 1 or 4 (4 total), and 4 of the numbers starting with 2 or 3 (8 total). In all, only 12 of the 24 possible numbers are allowed by the adjacent rule.
Wiki User
∙ 7y ago
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'let s be a collection of 16 integers, each from 1 to 30 inclusive. show that there must exist two distinct elements in s which differ by exactly 3. 'let s be a collection of 16 integers, each from 1 to 30 inclusive. show that there must exist two distinct elements in s which differ by exactly 3.
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