Seven-of-Eight Sums

★ 7/10combinatorics number theory Counting Modular Arithmetic

Problem

Let $a_1, a_2, \ldots, a_8$ be $8$ positive integers, and let

S = \left\{a_{i_1} + a_{i_2} + \cdots + a_{i_7} \mid 1 \leqslant i_1 < i_2 < \cdots < i_7 \leqslant 8\right\}

be the set of all sums of $7$ of them. If

S = \{82, 83, 84, 85, 86, 87, 89\},

find the sum of the largest and smallest of the $8$ integers.

Answer

Solution

Difficulty	7/10
Topics	combinatorics, number theory, Counting, Modular Arithmetic

Whiteboard

Your sketch is saved only in this browser. To share it, export your drawing as an image (whiteboard menu → Export as → PNG), then upload that image in the comments below.

Discussion

Ask questions, share alternate solutions, and use LaTeX freely.

0 comments

No comments yet.