# Dystopian Tax Collection

The year is 2081, and... oh, what can I say? Dystopian stories have been done to death.

I have a much more practical problem, though. I need to... gasp... pay my taxes.

I owe five different taxes: 1000 credits, 2250 credits, 2750 credits, 4000 credits, and 5000 credits.

What's a credit? Well, it's equivalent to a cubic millimeter of gold, so a cubic centimeter is 1000 credits.

I currently have a 5 centimeter by 3 centimeter by 1 centimeter bar of gold that I've dedicated to paying my taxes. It's worth exactly 15000 credits, and the total value of my taxes is also 15000 credits, so I should be fine.

However, I need to cut the bar into five parts so that each part is worth an amount equal to one of my taxes.

I bought one session at a laser cutter that can cut through and divide the gold, within the following rules:

1. The laser cutter has a maximum height of 1 cm. (So, I have to put it so that the 5 cm by 3 cm is facing upwards.)

2. I have three straight cuts, that all happen at the same time. I can't cut it heightwise, only the 5 cm by 3 cm area. I can't rearrange the gold bar in between the cuts.

3. Cuts must go completely through the cut surface. There is no starting point or ending point requirement.

• Do the cuts have to be straight? Dec 3 '18 at 15:22
• @hexomino yes, edited in. Dec 3 '18 at 15:22
• are we cutting only in equivalent pieces?
– user52327
Dec 3 '18 at 15:48
• @Jannis i'm not exactly sure what you mean... Dec 3 '18 at 15:56
• Does it have to be 5 pieces exactly? Or could I pay a particular tax with two (or more)smaller pieces? Dec 3 '18 at 16:18

Note: Numbers such as $$2,0833\ldots$$ represent recurring decimals so that, for example, $$2.0833\ldots = 2 \frac{1}{12}$$