Mr. P wants to build a clock in which the twelve numbers on the face are written as expressions of 1, 2, and 3.
The numbers 1, 2, and 3 must be used in order in each expression.
You may use
operations +, -, x, ÷ (or / for divided by), ^ (raised to a power), sqrt (square root),
! (factorial),
and int (or [ ] for greatest integer function), along with grouping symbols.
For example, the number zero could have been written as 1 + 2 - 3.
Solution to the Problem:
Here is Mr. P's clock:
Some of the possible answers:
1: 1^23 or -1 x 2 + 3
2: 1 - 2 + 3 or 12 / 3!
3: 1^2 x 3 or (-1 + 2) x 3
4: 12 / 3 or -1 + 2 + 3
5: -1 + 2 x 3 or 1 x 2 + 3
6: 1 x 2 x 3 or 1^2 x 3!
7: 1 + 2 x 3
8: 1 x 2^3
9: 12 - 3 or 1 + 2^3
10: 1 x [sqrt((2 + 3)!)]
11: -1 + 2 x 3! or sqrt(1 + (2 + 3)!)
12: (1 + 2)! + 3! or 1 x 2 x 3!
Correctly solved by:
| 1. James Alarie | Flint, Michigan |
| 2. Ivy Joseph | Pune, Maharashtra, India |
| 3. Jonathan Punke |
Joliet Central High School, Joliet, Illinois |
| 4. Kelly Stubblefield | Mobile, Alabama |
| 5. Bernice Rosales |
Delta High School, Delta, Colorado |
| 6. Nakoda Bird |
Mountain View High School, Mountain View, Wyoming |
| 7. Brijesh Dave | Mumbai City, Maharashtra, India |