Two players play a game with every bus number they see.
14
14
Player 1 doubles the bus number. Player 2 adds up its factors.
Whoever gets the largest total wins. Play the game with a friend.
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Topics: Starter  Arithmetic  Factors  Mental Methods  Mixed  Number
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Previous Day  This starter is for 28 April  Next Day
Bus Number 
Double  Factors  Sum of Factors  Winner 
1  2  1  1  Player 1 
2  4  1 2  3  Player 1 
3  6  1 3  4  Player 1 
4  8  1 2 4  7  Player 1 
5  10  1 5  6  Player 1 
6  12  1 2 3 6  12  Draw 
7  14  1 7  8  Player 1 
8  16  1 2 4 8  15  Player 1 
9  18  1 3 9  13  Player 1 
10  20  1 2 5 10  18  Player 1 
11  22  1 11  12  Player 1 
12  24  1 2 3 4 6 12  28  Player 2 
13  26  1 13  14  Player 1 
14  28  1 2 7 14  24  Player 1 
15  30  1 3 5 15  24  Player 1 
16  32  1 2 4 8 16  31  Player 1 
17  34  1 17  18  Player 1 
18  36  1 2 3 6 9 18  39  Player 2 
19  38  1 19  20  Player 1 
20  40  1 2 4 5 10 20  42  Player 2 
21  42  1 3 7 21  32  Player 1 
22  44  1 2 11 22  36  Player 1 
23  46  1 23  24  Player 1 
24  48  1 2 3 4 6 8 12 24  60  Player 2 
25  50  1 5 25  31  Player 1 
It is better to be Player 1! It is much easier to double a number than work out the factors and add them up and as you can see Player 1 is more likely to win.
Player 2 will only win when the bus number is an "abundant number". What is the next abundant number after 24?
Imagine you are the driver of a bus that begins its route with twelve passengers.
At the first stop one person gets off the bus and five people get on.
At the second stop two people get off the bus and seven people get on.
At the third stop nine people get off the bus and six people get on.
What is the name of the bus driver?
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Teacher, do your students have
access to computers? 

Here a concise URL for a version of this page without the comments.
Here is the URL which will take them to a student activity involving factors.
Transum.org/go/?to=Satisfaction