Math Olympiad 5

Number Thinking (2)( Week 28 Practice)

2. If 26 ≤ X ≤ 29, 10 ≤ Y ≤ 13, and 57 ≤ Z ≤ 63 with X, Y, and Z all being integers, what is the smallest value of

X − Y

3. Make a six-digit number using the digits 2,2,5,5,9,9. In the six-digit number, the identical digits must be separated by at least another non-identical digit and the larger digits must be separated by more digits than smaller ones. There are two such numbers, can you find them? The smaller one is . The larger one is .

4. 28's factorial is the product of all natural numbers from 1 through 28. Let M = 1 × 2 × 3... × 28. How many continuous zeroes will M have at its end?

5. A symmetrical number is a number that reads the same from either direction, e.g. 11, 121, 1221 are symmetrical numbers. How many 6-digit symmetrical numbers are divisible by 11?

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