Page 46 - NUMINO Challenge_B1

Basic Concepts Say the Target Number

Say the Target Number is a variation of the Nim game. The game is
played by two people taking turns saying numbers. The player who says
the target number wins.
The rules are shown below:

Rules

1. Set a target number.
2. The first player chooses a number from 1 to 4.
3. On the next turn, each player adds a number from 1 to 4 to

the opponent's number.
4. The player who says the target number wins.

Example Two players take turns saying numbers. The first player says a
number from 1 to 3. On the next turn, each player adds a number
from 1 to 3 to the opponent's number. If the target number is 50,
who is more likely to win: the first or the second player?

Class Notes

The greatest number that can be added is 3, and the smallest number that can be
added is 1. Therefore, in order to say the target number 50, a player has to say ,
which is less than 50 by , on his turn.

11 50

Winning number Target number

To say the number in , a player must say , which is less than that number by .

According to the strategy, saying numbers that are less than 50 by successively can

lead a player to win. The first number said will be , which is equal to the (quotient,

remainder) of 50 R.

In order to win, a player should always play (first, second) and start with the number .

Try It Again If the target number 35 wins the game presented in the
example above, what number should a player say first in order
to win?

43Puzzles and Games