# Candy Store on Five Drive

As an employee of the Candy Store on Five Drive, you send the store's amazingly famous chewy candy cubes all over the world. But you must pack them exactly as the eccentric owner, Fiver Cuube, has specified.

• Whenever you see 5 single chewy candy cubes, you put them in a bar.
• Whenever you see 5 bars, you put them in a flat.
• Whenever you see 5 flats, you put them in a box.
• Whenever you see 5 boxes, you put them in a carton.

0. Please draw pictures for the above conversions.

1. To keep track of the chewy candy cubes sent to customers, the ordering department uses the form below. Fill in the blanks in this ordering form.

 Order 1. 2. 3. 4. Cartons Boxes Flats Bars Singles Total 0 2 1 4 3 298 0 2 3 1 4 334 0 0 2 4 2 72 0 0 4 1 0 105

2. Fiver Cuube's head of ordering, Frances Indigo Violet Essen, is one smart cookie (figuratively speaking of course, we deal with chewy candy cubes not cookies!). She has found a way to condense the packaging numbers.

See if you can figure out the new system given in orders 1~4. When you understand the system, fill in the blanks in the orders 5~8.

Order Order 1. 5. Packaging Total Packaging Total 2143 298 10002 627 2314 334 1234 194 242 72 443 123 410 105 1414 234

3. Briefly explain how to use the packaging numbers to find the total number of candies.

4. Briefly explain how to use the total number of candies to find the packaging number.

5. Fiver Cuube hears about the new system and is impressed, but insists that a little "five" be put on each packaging number to remind customers that the Candy Store is on "Five" Drive. For example, the first packaging number would be $$\bf{2143_\text{five}}$$.

As a test, he would like to place thirty orders consisting of 1, 2, 3, … , and 30 total candies. Please give the thirty packaging numbers for Mr. Cuube, in order.