INTERNATIONL MATHEMATICS AND SCIENCE OLYMPIAD FOR PRIMARY SCHOOLS (IMSO) 2005

Answer the following 10 questions, and show your detailed solution in the space provided after each question. Each question is worth 4 points.
Time limit: 60 minutes.

1. In a mathematical competition consisting of 25 problems, 8 marks are given for each correct response, 0 marks for each incorrect response and each no response is awarded 3 marks. Tom scored 121 marks in this competition. What is the smallest number of incorrect responses he could have?

2. How many numbers less than 1000 have the product of their digits equal to 63?

3. The integers 1, 2, 3, .. , 2005 are written on the board. What is the smallest number of these integers that can be wiped off so that the product of the remaining integers ends in 8?

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