#209 Postman鈥檚 knock
Set by Maslanka
There was a knock at Professor Numero鈥檚 door. It was a postal worker.
Excuse me disturbing you, but can you help? This letter has a cryptic address. I can鈥檛 make head or tail of it:
鈥淭o the Resident, The house with a number whose digits when multiplied together give five times what they sum to, Long Road鈥�
The professor pondered. 鈥淲ell, you鈥檝e come to the right road. And, luckily, there鈥檚 only one house number in the road with this mathematical property 鈥� the one at the end, where Colonel Crypto lives.鈥�
As you would expect, the houses in Long Road are numbered consecutively from 1 upwards, with no missing numbers. How many houses are there in the road?
Solution next week
#208 Flower power
Solution
The blue and pink areas are the same, 16 square metres.
OBC is a right-angled triangle, so OB2 + OC2 = CB2, 2r2 = 42, r2 = 8. The area of triangle OBC = 4 square metres. The area of circle quadrant OBC = 录蟺r2 = 录蟺脳8 = 2蟺. The area of the clear segment is the area of the quadrant less the area of the triangle = 2蟺鈥�4. The area of the blue crescent is the area of the semicircle minus the area of the segment = 陆脳4蟺 鈥� (2蟺鈥�4) = 4 square metres. As this is the same as the area of the triangle, the four crescents together have the same area as the central square.
Quick quiz #189
set by Bethan Ackerley
1 The Hayflick limit is the number of times that certain cells can do what?
2 In cosmology, inflation is theorised to have begun approximately how soon after the big bang: 10-3600 seconds, 10-360 seconds or 10-36 seconds?
3 In which group of animals would you find the rumen, the reticulum, the omasum and the abomasum?
4 Who wrote the environmental science book Silent Spring, sparking a movement that led to a US-wide ban of the insecticide DDT?
5 In what year did Marie Curie win her first Nobel prize?
Quick quiz #189
Answers
1 Divide
2 10-36 seconds
3 In ruminants 鈥� they are the four sections of their stomach
4 Rachel Carson
5 1903