Learn Russian: У нас есть тридцать один билет.

In Russian, compound numbers that end in один (one), like тридцать один (thirty-one), are followed by a noun in the nominative singular form. Even though the logical meaning is plural, the grammar strictly agrees with that final word 'one'.

How is the word тридцать (thirty) formed?

Тридцать is made by combining три (three) and дцать (an old shortened version of ten). It literally means 'three tens'. You will see this -дцать ending in 20 and other tens as well!

If we were talking about a feminine noun like машина (car), would the number change?

Yes! Because the compound number ends in один, that final part must match the gender of the noun it counts. To say 'thirty-one cars', you would say тридцать одна машина, changing the masculine один to the feminine одна. The word тридцать stays the exact same.

Just to refresh, why does this sentence use У нас есть instead of a direct translation for 'We have'?

Russian rarely uses a direct verb for 'to have'. Instead, it uses the formula 'At [someone] there is'. У means 'at' or 'by', нас is the required form of 'we' after this preposition, and есть means 'there is'. So it literally translates to 'At us there is thirty-one ticket.'