No right angles in the shapes are in positions that could be corners of the completed square, so it must be the case that the corners of the square are made by putting two of the 45-degree corners together.
The outcome of Alice’s roll can be worked out by considering any one of the
three friends:
1. After the second roll Kai had 42 marbles. For him to finish with 41marbles, he must have given 1 marble to Alice as a result of Alice’s roll.
2. After the second roll Joe had 21 marbles. For him to finish with 20 marbles, he must have given 1 marble to Alice as a result of Alice’s roll.
3. After the second roll Alice had 27 marbles, so she must have received 2 marbles as a result of her roll (one from each of Kai and Joe).
Brian is 8 years old, so Eric must also be 8 years old as they are twins.
Lee must be 7 years old as he is 1 year younger than Eric.
Anita must be 10 years old as she is 3 years older than Lee.
To calculate the number of players who will get prizes, Sam has added the three prizes for positions to the prize that will be given out for a hole-in-one. However, it may be that the player who has scored a hole-in-one finishes in the top three and so receives two of the prizes.
If the person who stole the money must have had both an opportunity and a motive, then anyone who does not have either of those cannot be the person who stole the money.
