2023 AMC 8 Problems/Problem 6
Contents
Problem
The digits and
are placed in the expression below, one digit per box. What is the maximum possible value of the expression?
Solution 1
First, let us consider the case where is a base: This would result in the entire expression being
Contrastingly, if
is an exponent, we will get a value greater than
As
is greater than
and
the answer is
~MathFun1000
Solution 2
The maximum possible value of using the digits and
: We can maximize our value by keeping the
and
together in one power (the biggest with the biggest and the smallest with the smallest). This shows
(We don't want
because that is
.) It is going to be
~apex304, (SohumUttamchandani, wuwang2002, TaeKim, Cxrupptedpat, stevens0209, ILoveMath31415926535 (editing))
Solution 3
Trying all distinct orderings, we see that the only possible values are
and
the greatest of which is
~A_MatheMagician
Solution 4
There are two 2’s and one 3. To make use of them all, use 2 and 3 as the bases and 2 and 0 as the exponents.
~spacepandamath13
(Creative Thinking) Video Solution
~Education the Study of everything
Video Solution by Magic Square
https://youtu.be/-N46BeEKaCQ?t=5247
Video Solution by SpreadTheMathLove
https://www.youtube.com/watch?v=EcrktBc8zrM
Video Solution by Interstigation
https://youtu.be/1bA7fD7Lg54?t=331
Video Solution by WhyMath
~savannahsolver
See Also
2023 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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.