#161 Reduction deduction
鈥淲hen exactly is a person supposed to celebrate their half birthday?鈥� wondered Lionel. 鈥淚 mean, you could celebrate your 182/365th birthday, or your 183/365th birthday, but unless it is a leap year, the 1/2 fraction never arrives.鈥�
鈥淭he world鈥檚 greatest mystery,鈥� said Jill.
鈥淏ut the good news is that if you write every date as a fraction, so 1 January is 1/365 and 2 January is 2/365 and so on, then my birthday falls on a day where that fraction is reducible,鈥� says Lionel.
鈥凌别诲耻肠颈产濒别?鈥�
鈥淵ou know, can be simplified, like 12/18 can be reduced to 2/3. My birthday fraction can be reduced, but the next day can be reduced even more, to numbers on the top and bottom that are even smaller.鈥�
鈥淚鈥檒l be sure to celebrate by reducing the number of presents I get you,鈥� says Jill.
When is Lionel鈥檚 birthday?
#160 Blurry-Ness
Solution
The correct answer is 15 metres.
When the boat reaches the ripple (point X), the ripple has been travelling for 5 seconds. When the boat crosses the other side (Y), the ripple has been travelling for 15 seconds, so the diameter of the outer ripple in the diagram is three times that of the inner ripple, so the ripple originated 1/4 of the way between X and Y. The boat took 10 seconds to cross the ripple, so reached Nessie 2.5 seconds after crossing the ripple or 7.5 seconds after taking the photo. This gives 2 m/s x 7.5 s = 15 metres.
Quick quiz #145
1 How many types, or flavours, of quark are there?
2 The two types of vascular tissue in plants are the xylem and the what?
3 Following humans and chimpanzees, what was the third ape species to have its genome sequenced?
4 The layered, fossilised structures created when microbes are overlaid with sediment are known as what?
5 Where in our solar system would you find Makemake and Orcus?
Answers
1 Six: up, down, charm, strange, top and bottom
2 Phloem
3 The Sumatran orangutan (Pongo abelii)
4 Stromatolites
5 The Kuiper belt, the ring of objects located beyond Neptune
Solution next week