The last digit of each number is 6. What is the condition for the product of the two numbers to end in 36?

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In the product, the last two digits are influenced only by the last two digits of the multiplicand and the multiplier; therefore, it is sufficient to examine the product of two two-digit numbers. Let these numbers be $10a+6$ and $10b+6$; then

$$
(10a+6)(10b+6) = 100ab + 60(a+b) + 36
$$

This number ends in 36 if $60(a+b)$ is a multiple of 100, that is, if $a+b$ is a multiple of 5. Thus, the necessary and sufficient condition is that the sum of the digits in the tens place be $0, 5, 10$ or 15.

(Fuchs István, Beregszász.)

Number of solutions: 35.