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.

  • $\begingroup$ Do the cuts have to be straight? $\endgroup$
    – hexomino
    Dec 3, 2018 at 15:22
  • $\begingroup$ @hexomino yes, edited in. $\endgroup$ Dec 3, 2018 at 15:22
  • $\begingroup$ are we cutting only in equivalent pieces? $\endgroup$
    – user52327
    Dec 3, 2018 at 15:48
  • $\begingroup$ @Jannis i'm not exactly sure what you mean... $\endgroup$ Dec 3, 2018 at 15:56
  • $\begingroup$ Does it have to be 5 pieces exactly? Or could I pay a particular tax with two (or more)smaller pieces? $\endgroup$ Dec 3, 2018 at 16:18

1 Answer 1


I think this would work

enter image description here
where the numbers on each side represents the number of centimetres left by each cut.

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

  • 2
    $\begingroup$ There are an infinite number of solutions, so I think the original problem should have an extra constraint added. For example: 4. Operating the laser is expensive so use the shortest possible total length of cuts. If that is added then hexomino's solution is nearly optimal, rotating the top left cut to an angle of 45 degrees (so it still separates 1000 mm^2) would do the trick. $\endgroup$
    – Penguino
    Dec 3, 2018 at 21:26

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