In the grid below, box A shares walls or corners with 3 other boxes, B, E, and F. Determine how many walls or corners each of the other boxes share.
Solution
What would the numbers be in a 5 x 5 grid?
Problem of the Month - June 2026
Look at the following row of numbers:
10, 15, 21, 4, 5
They are arranged so that each pair of adjacent numbers adds up to a square number:
10+15=25
15+21=36
21+4=25
4+5=9
Can you arrange the numbers 1 to 17 in a row in the same way, so that each adjacent pair adds up to a square number?
Source: NRICH
Problem of the Month - April 2026
Pick any 3 numbers from the following list, circle them, and find their sum
1 , 1 , 1 , 4 ,4 , 4, 7 , 7 , 7, 10, 10 ,10
Repeat the process with a new set of numbers from the original list.
What do you notice about the sums?
Can you explain why this happens?
Answer:
The sum is always a multiple of 3.
Problem of the Month - May 2026
Each number from 1 to 6 replaces one of the letters P, Q, R, S, T, and U.
The sum of P and Q is 5 and the difference between R and S is 5.
If T is greater than U, what number replaces the letter T?
Source: 2023 Gauss Math Contest
Answer:
Since the sum of P and Q is 5, P and Q must be 1 and 4 or 2 and 3.
Since the difference between R and S is 5, R and S must be 1 and 6.
This means that P and Q must be 2 and 3.
Problem of the Month - March 2026
Five different numbers in a list have a median of 10 and a range of 7.
What is the smallest possible number in the list?
Source: 2024 Gauss Math Contest
Problem of the Month - February 2026
Imagine two red frogs and two blue frogs sitting on lily pads, with an empty lily pad in between them.
Frogs can slide onto an empty lily pad that is beside them or jump over a frog onto an empty lily pad.
Frogs can't jump over more than one frog.
Frogs can jump forward or backwards