# Difference between revisions of "2002 AMC 12B Problems/Problem 10"

## Problem

How many different integers can be expressed as the sum of three distinct members of the set $\{1,4,7,10,13,16,19\}$? $\mathrm{(A)}\ 13 \qquad\mathrm{(B)}\ 16 \qquad\mathrm{(C)}\ 24 \qquad\mathrm{(D)}\ 30 \qquad\mathrm{(E)}\ 35$

## Solution

We can make all multiples of three between 1+4+7=12 and 13+16+19=48, inclusive. There are $\frac{48}{3}-\frac{12}{3}+1=13\Rightarrow \boxed{\mathrm{(A)}$ (Error compiling LaTeX. ! File ended while scanning use of \boxed.) integers we can form.

Invalid username
Login to AoPS
{"ft_lang_label":"__label__en","ft_lang_prob":0.7034087,"math_prob":0.99895424,"size":1027,"snap":"2021-04-2021-17","text_gpt3_token_len":356,"char_repetition_ratio":0.12218964,"word_repetition_ratio":0.32857144,"special_character_ratio":0.39922103,"punctuation_ratio":0.11165048,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99781317,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,10,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-20T19:39:12Z\",\"WARC-Record-ID\":\"<urn:uuid:d3df82b2-e94e-4aec-a452-cd46a68e44b5>\",\"Content-Length\":\"38478\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:55d5ebe6-a139-41d0-b629-fc1f66e15900>\",\"WARC-Concurrent-To\":\"<urn:uuid:678927c7-230e-4319-8f57-da200d72f1df>\",\"WARC-IP-Address\":\"104.26.10.229\",\"WARC-Target-URI\":\"https://artofproblemsolving.com/wiki/index.php?title=2002_AMC_12B_Problems/Problem_10&diff=22978&oldid=22928\",\"WARC-Payload-Digest\":\"sha1:AOABBTK2RA454TJIHE4KDSXE7OIQOCL7\",\"WARC-Block-Digest\":\"sha1:QD5ERI2KYFBVRQRFJ4KLGD463OXV6FYN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618039490226.78_warc_CC-MAIN-20210420183658-20210420213658-00255.warc.gz\"}"}