Traveller's gold bar riddle

22 Jan 2018

On your holiday, you arrive in Glenorchy (a small town in the South Island of New Zealand). You need to stay for 7 nights at a hotel but you only have 1 straight gold bar. The hotel manager asks you to pay her 1/7th of the gold bar every night at 6pm before you sleep. And to make matters worse, you are given a saw but are only allowed to make two cuts.

How do you cut the bar and pay for your stay?

Solution below

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Solution:

With your two cuts, slice the gold bar into 4/7th 2/7ths and 1/7th. On your first night, give the inn keeper the 1/7th, on the second night give the inn keeper the 2/7th in exchange for the 1/7th. Third night give the 1/7th again, fourth night give the 4/7th and get back the 1/7th and 2/7ths. Now repeat the first steps for the last three nights.

Extension:

Determine a way to stay 100 nights giving 1/100th of a bar each night, using only 2 cuts.

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Extension solution:

Cut the gold bar on an angle around its length, such that you don’t go completely through it but loop around 50 times. With the second cut, you slice completely down the length make 98 identical pieces (and the ends add up to the last two pieces).

Other solutions:

The gold bar extends around the whole world lapping over itself (i.e. it is in curved space), therefore a single cut makes multiple pieces.