What-is-the-number-of-triples-a-b-c-of-positive-integers-such-that-i-a-lt-b-lt-c-lt-10-and-ii-a-b-c-10-form-the-sides-of-a-quadrilateral-

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Question Number 20810 by Tinkutara last updated on 03/Sep/17

What is the number of triples (a, b, c) of positive integers such that (i) a < b < c < 10 and (ii) a, b, c, 10 form the sides of a quadrilateral?

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{triples}\:\left({a},\:{b},\:{c}\right)\:\mathrm{of} \\ $$$$\mathrm{positive}\:\mathrm{integers}\:\mathrm{such}\:\mathrm{that} \\ $$$$\left(\mathrm{i}\right)\:{a}\:<\:{b}\:<\:{c}\:<\:\mathrm{10}\:\mathrm{and}\:\left(\mathrm{ii}\right)\:{a},\:{b},\:{c},\:\mathrm{10}\:\mathrm{form} \\ $$$$\mathrm{the}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{a}\:\mathrm{quadrilateral}? \\ $$

Commented by Tinkutara last updated on 04/Sep/17