7.4. Find the smallest natural number ending in the digit 4 that quadruples when its last digit is moved to the beginning of the number.
# 7.4. Answer: 102564

If a number ending in 4 is multiplied by 4, the result is a number ending in 6, so the last digits of the desired number are 64. If such a number is multiplied by 4, the result is a number ending in 56, so the desired number ends in 564. Continuing to restore the number in this way, it turns out that the desired number should end in 102564. The smallest number ending with these digits is 102564. Comments on evaluation.

Answer only: 3 points. Answer and the observation that the number can be restored from the end: 4 points.

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