Tasks

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TASKS

1. A census agent knocked on the door of a house and asked the man who answered the door if anyone other than himself lived in the house. The man replied: “Yes, there are three more baitfish of different ages here. The sum of their ages is equal to the number of this house (which the census agent knew), and the product of their ages is 1296.” After some calculations, the agent asked one more question and left. He set the ages. What is the number of this house?

2. When runners $A, B$ and $C$ participate in a 100-meter race. When $A$ finished, $B$ was 10 meters behind him, and when $B$ finished, $C$ was 10 meters behind him. How far was $C$ from $A$ when $A$ finished? It is assumed that everyone runs at a constant speed.

3. Determine the number $A$ using two division operations, where each asterisk represents a number from 0 to 9.

4. The four lies $A, B, C$ and $D$ tell the truth only once out of three times. $A$ said that $B$ denies, which $C$ claims that $D$ agreed. What is the probability that $D$ told the truth? Show that this probability is equal to the probability that $A, B, C$ each individually told the truth.