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4 problems match “digit problems”. Clear

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1. Inserting a zero into a two-digit number ●○○○○ 10 ptsAnička and Blanka each wrote a two-digit number starting with a seven, and the two girls chose different numbers. Each inserted a zero between the two digits, creating a three-digit number. From this three-digit number, each subtracted their original two-digit number. Both girls got the same result. What was this result?
2. Average speed from milestones ●●○○○ 20 ptsA car travels at a uniform speed. The driver sees a milestone showing a two-digit number $XY$. One hour later the driver sees a milestone showing the same digits in reverse order, $YX$. One hour after that the driver sees a milestone showing a three-digit number $X0Y$, with a 0 between the same two digits. What is the speed of the car, in km/h?
3. Greatest number from two sequences ●●○○○ 20 ptsWhat is the greatest three-digit number $\overline{abc}$ such that $4, a, b$ form a geometric sequence and $b, c, 5$ form an arithmetic sequence? Here $a$, $b$, $c$ are digits.
4. Primes from up to two digits ●●○○○ 20 ptsPick one or two different digits from the set $\{1, 3, 6, 7\}$ and arrange them to form a number. How many prime numbers can be created in this manner?