Veverka Hryzka ate the nuts from her supplies in the following way:

- $\mathrm{v}$ on a diet day, she ate one nut,
- on a normal day, she ate two more nuts than on a diet day.

For a certain 19 consecutive days, diet and normal days alternated regularly.

Determine the maximum and minimum number of nuts Hryzka could have eaten during these 19 days.

(E. Novotná)
Veverka ate one nut on a diet day and three nuts on a normal day. Both types of days alternated regularly, so the type of day that started the 19-day period repeated 10 times, and the other type repeated 9 times.

Since we do not know whether the observed period started with a diet day or a normal day, we must consider both possibilities:

a) if it started with a diet day, the squirrel ate $10 \cdot 1 + 9 \cdot 3 = 37$ nuts,

b) if it started with a normal day, the squirrel ate $10 \cdot 3 + 9 \cdot 1 = 39$ nuts.

The squirrel ate at least 37 and at most 39 nuts.

Scoring suggestion. 1 point for the number of nuts eaten on a normal day; 2 points for the total number of nuts eaten in each of the possibilities; 1 point for the conclusion.