Did You Find Out? Get the Answer to the Riddle of E-News Issue No. 6, November 2015
What is Tom's share of the gold claim?
Mike's gold claim diagonally overlaps Tom‘s claim.
Gold Prospector Mike has found a promising vein of gold. He would like to keep the gold find for himself, but due to an error in the initial land survey, his claim diagonally overlaps with his neighbor Tom‘s claim (see sketch). A corner of Tom‘s rectangular claim is located right in the center of Mike‘s square-format claim.
In order to avoid legal disputes, Mike has agreed that Tom gets a share of the gold find. This percentage is calculated from half of the overlapping area based on the entire area of Mike's claim. What is Tom‘s share?
Solution
Turn Tom‘s claim around the corner to get to the solution.
Rotate Tom‘s claim around the corner so that the sides of both claims are parallel to each other. Now it is clear that Tom's claim overlaps a quarter of Mike’s claim. This proportion does not vary by rotation because the lost triangle is congruent to the additional triangle. As agreed, Tom gets a share based on half of the overlapping area. Thus, Tom receives half of the quarter (1/8) and gets 12.5 % of the gold find.
Pepperl+Fuchs Oy
Areenakatu 7
FI-37570 Lempäälä
Finland
info@fi.pepperl-fuchs.com
+358 20 7861 290
info@fi.pepperl-fuchs.com
+358 20 7861 291
Pepperl+Fuchs on dynaaminen ja tulevaisuuteen suuntaava yritys joka myy konepajateollisuuden, robotiikan ja teollisuusautomaation komponentteja. Tuotannon sujuvuus, tuotteiden korkea laatu ja niiden maailmanlaajuinen saatavuus ovat tuoneet yritykselle menestystä jo yli 70 vuoden ajan. Pepperl+Fuchs työllistää maailman laajuisesti yhteensä noin 6300 henkilöä. Globaalilla yrityksellä on tuotantolaitoksia Saksassa, Singaporessa, Yhdysvalloissa, Unkarissa, Indonesiassa ja Vietnamissa, joista suurin osa ovat ISO 9001-sertifioitu.