#102 Passport to success
My nine-digit passport number has some remarkable properties. Not only does it use all the digits from 1 to 9, but if I label the number ABCDEFGHI, then:
A is divisible by 1
AB is divisible by 2
ABC is divisible by 3
ABCD is divisible by 4
ABCDE is divisible by 5
ABCDEF is divisible by 6
ABCDEFG is divisible by 7
ABCDEFGH is divisible by 8
ABCDEFGHI is divisible by 9
You could program a computer to find this passport number, but there are shortcuts to figuring it out with a pen and paper. For example, a number is only divisible by 3 if its digits add up to a multiple of three (eg: 372 is divisible by 3 because 3+7+2=12). And a number is only divisible by 4 if its last two digits form a number that is also a multiple of four (hence 9324 is divisible by 4 because 24 also is.)
What is my passport number?
Solution next week
Quick quiz #90
1 Which species of whale has the largest mouth?
2 In October 2020, NASA announced that water particles had been found in which crater of the moon?
3 Name the type of starch that dominates in sticky rice.
4 What invention is US deep sea diver Otis Barton best known for?
5 How many elements were in Dmitri Mendeleev鈥檚 original periodic table in 1869?
Answers:
1 The bowhead whale. Its mouth can be almost 5 metres long, 4 metres high and 2.5 metres wide
2 Clavius
3 Amylopectin
4 The bathysphere submersible
5 63
#101 Red triangle
The red and blue triangles in the illustration have the same length of base and height, so have the same area. By the same argument, the blue triangle and triangle ABC have the same area.
But ABC is half B the area of square ABCD, and ABCD is four times the C area of the small square
