A brain teaser.

Background

  • Ok. % means "out of 100", right? So 5% is really 5/100. And 5% = 5 "per cent" = 5 per "100", or 5 per 10^2. In other words, our "100" is actually (fingers)^(hands).
  • It is impossible to allow 3 consecutive discounts (using our "per cent") and end up with EXACTLY half the amount we started with. We can come close, but it cannot equal exactly half. For example, if you take away 10% of 3000 (2700.00) then take away 15% of that (2295.00) and then take away 35% of that you get 1491.75. Close to half, but not quite.

Problem:

  • On Planet X (fingers)^(hands) != 100. It is k. On Planet X, k is such that 3 different discounts can be applied as shown above, and the result is exactly half. Residents of Planet X have 3 hands, and each hand has more than one finger. Find the 3 discounts, using the minimum case.
Answer to Planet X Fingers

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