MathDB

4

Part of 2023 LMT Fall

Problems(2)

2023 Fall LMT Team #4 positive two-digit number

Source:

2/4/2024
Fred chooses a positive two-digit number with distinct nonzero digits. Laura takes Fred’s number and swaps its digits. She notices that the sum of her number and Fred’s number is a perfect square and the positive difference between them is a perfect cube. Find the greater of the two numbers.
number theory
2023 Fall Speed p4

Source:

12/23/2023
The numbers 11, 22, 33, and 44 are randomly arranged in a 22 by 22 grid with one number in each cell. Find the probability the sum of two numbers in the top row of the grid is even.
Proposed by Muztaba Syed and Derek Zhao
Solution. 13\boxed{\dfrac{1}{3}} Pick a number for the top-left. There is one number that makes the sum even no matter what we pick. Therefore, the answer is 13\boxed{\dfrac{1}{3}}.
2023FAlLspeedCombo