Earlier today I set you some problems on “guardian numbers.” Here they are again with solutions.
The definition: 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
(For all the questions, consider only the numbers 1, 2, 3, 4, and so on.)
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?
Solutions a) 18, 87, 180. b) 19, 20, also 199, 200, and so on. c) one (the number 1)
A number’s grandguardian is their guardian’s guardian.
d) Who is the grandguardian of 499?
e) Whose grandguardian is 900?
Solutions d) 505, e) 898
Two numbers are cousins if they have the same grandguardian but different guardians.
f) What is the smallest pair of cousins?
Solution f) 28, 30
Thanks again to Daniel Griller, who set today’s puzzle and came up with the idea of number guardians. Check out his book 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.
