Difference between revisions of "2024 AMC 8 Problems/Problem 8"
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==Video Solution 1 (easy to digest) by Power Solve== | ==Video Solution 1 (easy to digest) by Power Solve== | ||
https://youtu.be/16YYti_pDUg?si=5kw0dc_bZwASNiWm&t=121 | https://youtu.be/16YYti_pDUg?si=5kw0dc_bZwASNiWm&t=121 | ||
+ | |||
+ | ==Video Solution by NiuniuMaths (Easy to understand!)== | ||
+ | https://www.youtube.com/watch?v=V-xN8Njd_Lc | ||
+ | |||
+ | ~NiuniuMaths | ||
==Video Solution 2 by SpreadTheMathLove== | ==Video Solution 2 by SpreadTheMathLove== |
Revision as of 01:08, 27 January 2024
Contents
[hide]Problem
On Monday Taye has $2. Every day, he either gains $3 or doubles the amount of money he had on the previous day. How many different dollar amounts could Taye have on Thursday, 3 days later?
Solution 1 (BRUTE FORCE)
How many values could be on the first day? Only dollars. The second day, you can either add
dollars, or double, so you can have
dollars, or
. For each of these values, you have
values for each. For
dollars, you have
dollars or
, and for
dollars, you have
dollars or $
. Now, you have
values for each of these. For
dollars, you have
dollars or
, for
dollars, you have
dollars or
, for
dollars, you have
dollars or
, and for
dollars, you have
dollars or
.
$ and $
repeat leaving you with
different values.
~ cxsmi (minor formatting edits)
Solution 2 (Slightly less BRUTE FORCE)
Continue as in Solution 1 to get ,
, or
dollars by the 2nd day. The only way to get the same dollar amount occurring twice by branching (multiply by
or adding
) from here is if
or
which both aren't true. Hence our answer is
.
~ Sahan Wijetunga
Video Solution 1 (easy to digest) by Power Solve
https://youtu.be/16YYti_pDUg?si=5kw0dc_bZwASNiWm&t=121
Video Solution by NiuniuMaths (Easy to understand!)
https://www.youtube.com/watch?v=V-xN8Njd_Lc
~NiuniuMaths
Video Solution 2 by SpreadTheMathLove
https://www.youtube.com/watch?v=L83DxusGkSY
Video Solution by CosineMethod [🔥Fast and Easy🔥]
https://www.youtube.com/watch?v=alDY4yhaEEg
See Also
2024 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.