4. If a two-digit number is decreased by 36, the result is a two-digit number with the same digits but in reverse order. In the answer, specify the arithmetic mean of the resulting number sequence.

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# Solution.

$\overline{x y}=10 x+y-$ the original two-digit number, then $\overline{y x}=10 y+x-$ the number written with the same digits but in reverse order. We get the equation $10 x+y=10 y+x+36$

From the equation, it is clear that the two-digit number is greater than 36. Let's start the investigation with the tens digit equal to 4.

| $\boldsymbol{X}$ | equation | $\boldsymbol{y}$ | number |
| :---: | :---: | :---: | :---: |
| 4 | $40+y=10 y+4+36$ | $y=0$ | 40 does not fit the condition |
| 5 | $50+y=10 y+5+36$ | $y=1$ | 51 |
| 6 | $60+y=10 y+6+36$ | $y=2$ | 62 |
| 7 | $70+y=10 y+7+36$ | $y=3$ | 73 |
| 8 | $80+y=10 y+8+36$ | $y=4$ | 84 |
| 9 | $90+y=10 y+9+36$ | $y=5$ | 95 |

These could be the numbers $51,62,73,84,95$. The arithmetic mean is 73.

Answer: 73.