Star Operation with Cubes
Pro Problems > Math > Number and Quantity > Number Theory > Star OperationsStar Operation with Cubes
Solution
In order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.
Similar Problems
Hashtag Operation
Non-Commutative Operation
x ♦ 2x = 2x ♦ x.
Note that this operation is not commutative; the order of operands cannot be exchanged without altering the result of the operation.
Guess the Star
There exists a star (*) operation for which the following equations are true:
2 * 3 = 10
5 * 2 = 35
3 * 6 = 27
8 * 7 = 120
Find a star operation rule which satisfies all of these equations, and then use your rule to calculate the following:
10 * 11 = ?
h and k
x * y = x2 - y2 + kx - hy. If 5 * 2 = 48 and 4 * 3 = 30, find the ordered pair (h, k).
Triangular Operation
The arrangementStar and Pound Operations
If a * b = (a + b)2, and a # b = (a - b)2, find x such that (2 * x) # (x * 1) = 81
Diamond Operation
If the operation ♦ is defined as follows: a ♦ b = a2 - b2 , and 
18 ♦ (x ♦ 8) = 6 ♦ 1, find all possible values of x.
Commutative Operation
The operation * is defined as follows: x * y = (ax + b)(by + a), for some real numbers a and b. Under what conditions is this operation commutative?
Fractional Operation
Blogs on This Site
Like us on Facebook to get updates about new resources