2023 AMC 8 Problems/Problem 4
Contents
- 1 Problem
- 2 Solution 1
- 3 Solution 2
- 4 Simple, Intuitive Solution by MathTalks_Now
- 5 Video Solution (How to Creatively THINK!!!)
- 6 Video Solution by Math-X (Smart and Simple)
- 7 Video Solution by Magic Square
- 8 Video Solution by SpreadTheMathLove
- 9 Video Solution by Interstigation
- 10 Video Solution by WhyMath
- 11 Video Solution by harungurcan
- 12 See Also
Problem
The numbers from to are arranged in a spiral pattern on a square grid, beginning at the center. The first few numbers have been entered into the grid below. Consider the four numbers that will appear in the shaded squares, on the same diagonal as the number How many of these four numbers are prime?
Solution 1
We fill out the grid, as shown below: From the four numbers that appear in the shaded squares, of them are prime: and
~MathFun1000, MRENTHUSIASM
Solution 2
Note that given time constraint, it's better to only count from perfect squares (in pink), as shown below: From the four numbers that appear in the shaded squares, of them are prime: and
~TheMathGuyd
Simple, Intuitive Solution by MathTalks_Now
- *Different Solution not shown before!*
https://studio.youtube.com/video/PMOeiGLkDH0/edit
Video Solution (How to Creatively THINK!!!)
~Education the Study of everything
Video Solution by Math-X (Smart and Simple)
https://youtu.be/Ku_c1YHnLt0?si=cc_Ii2j2pmT6wOuZ&t=412
~Math-X
Video Solution by Magic Square
https://youtu.be/-N46BeEKaCQ?t=5392
Video Solution by SpreadTheMathLove
https://www.youtube.com/watch?v=EcrktBc8zrM
Video Solution by Interstigation
https://youtu.be/DBqko2xATxs&t=233
Video Solution by WhyMath
~savannahsolver
Video Solution by harungurcan
https://www.youtube.com/watch?v=35BW7bsm_Cg&t=402s
~harungurcan
See Also
2023 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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.