How can you pay for your ticket home with the exact change.
If you recall the Argond system of currency used twenty five different coins. Although I didn't show you every different available coin I made sure to show you the five different symbols, and five different colours which make up the currency. It shouldn't have been a big leap to realise that if each colour is paired with each shape once, you get the twenty-five different pieces stated in the puzzle.
Here are the twenty five different coins which make up the currency on Arg, arranged in a logical order. This is important as working logically, as the Argonds would, is the only way to get your head around the currency.
We were implicitly told the value of four of the pieces in the puzzle, and told that two further pieces added up to the same value.
This is our diagram updated with the information we have. You might have been looking for a simultaneous equation style method to solving this puzzle. That method just wont work since you have too many variables and not enough data. What you needed to do was work out the reasoning behind the numbering. In the UK we put a five on a bank note because it's worth five pounds and five is the symbol for 'five'. Why therefore is a green circle, a red square or an orange crescent the symbol for four?
If might not seem a lot, but if we take a few logical leaps we can come up with a reasonable solution. It should not have escaped your notice that the fourth item in the first column is worth four. Similarly the first item in the fourth row is worth four. However, the other four is the second item in the second column.
In other words items 1x4, 4x1 and 2x2 are all fours. When you write it like that it seems obvious doesn't it. The value of a coin is its row multiplied by its column. Except, I chose the arrangement of the pieces in this grid, if I had swapped the crescents and the pentagons, or the blues and the greens it wouldn't work. So why is this arrangement the right one?
Well, the pieces are arranged in columns according to how many sides they have, indeed this is the first number you multiply to get the value. The pieces are also arranged in rainbow order and again, it is the position int he rainbow which you must multiply by to get the value.
So to pay your thirty-three Drogna fair you need just proffer the blue square which is worth 16, the yellow triangle worth 9 and the orange square worth 8.
That's not all the fun that can be had with the Argond currency mind you. So if you've enjoyed tackling the nuances if number and shape, then try and solve these problems.
What is the smallest value, greater than one, that cannot be made up from two Drogna?
What is the smallest value, greater than two, that cannot be made up from three Drogna?