Tell the ones place digit of the answer in 47^2020 (47 to the power 2020)
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youblundered_XD wrote:
Tell the ones place digit of the answer in 47^2020 (47 to the power 2020)
The ones digits go in repeating sets of four: 7, 9, 3, 1, and since 2020 = 0 (mod 4), then the ones place of 47^2020 would be 1.
This one stumped me during the amc10b
Bela and Jenn play the following game on the closed interval ![$[0, n]$](https://images.chesscomfiles.com/proxy/latex.artofproblemsolving.com/a/5/8/a585433224883cbcd304f34129a152b97d5ed96e/https/08e74920c1.png)
of the real number line, where 
is a fixed integer greater than 
. They take turns playing, with Bela going first. At his first turn, Bela chooses any real number in the interval . Thereafter, the player whose turn it is chooses a real number that is more than one unit away from all numbers previously chosen by either player. A player unable to choose such a number loses. Using optimal strategy, which player will win the game?
Diffy Q's or Abstract Geometry problem ???
Feb 15, 2020
0
#6
Before looking up the official solution, this is what I came up with for Problem 16 on the 2020 AMC 10B, which was posted by @1e41-O in comment #4.
(A) Bela [the first player] will always win.
The first player starts by selecting n/2 as the first choice. If the second player chooses x on any turn, then the first player chooses n-x on the next turn.
Note that you can generalize the problem and let n be any positive real number. The players still play on the interval [0,n] and all other rules remain the same. The first player will still win using the same strategy.
This is the link to the problem and official solution.
Give a hard math question,whoever gives the hardest wins 1 pi.