Numbers can be odd, even, prime, square, natural, perfect, complex, rational…and as from today they can also be guardians.
Let the numbers be 1, 2, 3, 4, and so on. The guardian of x is the next number that shares at least one digit of x.
For example: the guardian of 4 is 14, and the guardian of 59 is 65.
Guardian figures
a) Find the guardian of 17, the guardian of 79, and the guardian of 179.
b) Find two consecutive numbers with the same guardian.
c) How many numbers are exactly 9 less than their guardian?
A number’s grandguardian is their guardian’s guardian.
d) Who is the grandguardian of 499?
e) Whose grandguardian is 900?
Two numbers are cousins if they have the same grandguardian but different guardians.
f) What is the smallest pair of cousins?
I’ll be back with the solutions at 5pm. Please NO SPOILERS. Instead please share your favourite type of number or invent your own.
UPDATE: Read the solutions here.
The idea of guardian numbers is due to the brilliant puzzle setter Daniel Griller. His most recent book is A Ring of Cats and Dogs.
I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
