Slash and Dash Numbers
The table pairs two positional number systems. How does the left column's number system work?
To demonstrate your solution, please give in decimal the sum of
/-\ / and \ \ \ .
Any addition of spaces within the numbers is solely for reasons of display.
| - | 0 |
| / | 1 |
| /\ | 2 |
| /- | 3 |
| // | 4 |
| /\ \ | 5 |
| /\ - | 6 |
| /\/ | 7 |
| /-\ | 8 |
| /-- | 9 |
| /-/ | 10 |
The answer is 12.
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1 solution
The number system is my way of writing balanced ternary: base 3, but using -1,0,1. Balanced ternary lets you write any number using -1, 0, and 1, which often makes arithmetic easy. The system also has neat properties, such as you can check if a number is even by whether the sum of its digits are even. Naturally, since it is base 3, numbers ending in 0 are divisible by 3. This way of writing it is quick. Negative numbers are simply upside down: // is 4; \ \ is -4. Puzzlers already familiar with positional notation and negative numbers are ready for this one; I would recommend just asking them to explain it when communication suits more than a number answer.
To explain the characters and their positional system, / is 1, - is 0, \ is negative 1. Like the hundreds come to the left of the tens in decimal positions, the positions increase toward the left as powers of three, like ternary. E.g., similar to decimals hundreds, tens, and ones places, if you used three digits in balanced ternary you'd have the 3^2=9s place at left, the 3^1=3s place in the middle, and the 3^0=1s place. Like in decimal, the values in the positions sum to make the number they represent, like in "11" one 10 plus one 1 is 11.
For instance, / \ - is six. It takes three places and one of each possible character to make the value 6 in balanced ternary. From the left, / (1) is in the 9s place, a value of 9. \ (-1) is middle the 3s place, a value of -3. - (0) is in the 1s place, a value of 0. 9-3+0=6.
For other examples, /// is 9+3+1=13. \ \ \ is -9-3-1=-13. /-\/ is 27+0-3+1=25.
So, the answer to the puzzle's /-\ / (25) and \ \ \ (-13) is 12.
Briefly on the day I posted it, this problem was up with an erroneous solution; sorry if anyone was bothered. I apologize that I don't know why, but it did seem to me that what I put in the answer field kept reverting to a value I did not want to put in. Additionally, displaying slashes seems to give Brilliant difficulties in this explanation, too.