Sunday Afternoon Maths XXXII
Posted on 2014-10-19
Frogs
Source: nrich
Two frogs and two toads are standing on five lily pads.
![](javascript:showlimage("frogs-and-toads.png"))
The frogs and toads need to pass each other. They can only move by jumping one or two lily pads forward. In jumping two pads forwards they can jump over other frogs or toads.
How many jumps need to be made to get the frogs and toads past each other?
The blue-eyed sisters
If you happen to meet two of the Jones sister (two sisters chosen at random from all the Jones sisters), it is exactly an even-money bet that both will be blue-eyed. What is your best guess of the total number of Jones sisters?
1089
Take a three digit number. Reverse the digits then take the smaller number from the larger number.
Next add the answer to its reverse.
For example, if 175 is chosen:
$$571-175=396$$
$$396+693=1089$$
What numbers is it possible to obtain as an answer, and when will each be obtained?
If you enjoyed these puzzles, check out Advent calendar 2023,
puzzles about complex numbers, or a random puzzle.
puzzles about complex numbers, or a random puzzle.