Radovan is reading an interesting book. Yesterday he read 15 pages, today another 12 pages. To his surprise, he realized that the sum of the page numbers he read yesterday is the same as the sum of the page numbers he read today. Which page will he start reading tomorrow? (Radovan does not skip any pages or read any page twice. He never ends a day's reading in the middle of a page.)

(M. Petrová)
It is evident that the pages Radovan read today have higher numbers than those he read yesterday. The first page read today has a number 15 higher than the first page read yesterday. ("In between" are the remaining 14 pages he read yesterday.) The second page read today again has a number 15 higher than the second page read yesterday. (The number of each of them has increased by one.) We can reason similarly — everything is symbolically illustrated in the following scheme:

Pages read yesterday: $1.2 .3 .4 .5 .6 .7 . \quad 8.9 .10 .11 .12 .13 .14 .15$.

Pages read today: $1.2 .3 .4 . \quad 5.6 .7 . \quad 8.9 .10 .11 .12$.

Since the sum of the numbers of the pages read yesterday must equal the sum of the numbers of the pages read today, the sum of the numbers on the 13th, 14th, and 15th pages read yesterday must equal the sum of the "increases" of the previous twelve pages. This means that the sum of the numbers of the last three pages read yesterday is equal to $12 \cdot 15=180$. If the sum of three consecutive natural numbers is 180, the middle one is $180: 3=60$, the smallest is 59, and the largest is 61. We can easily calculate that Radovan read pages numbered 47 to 61 yesterday, and pages numbered 62 to 73 today. Tomorrow he will start reading page number 74.

Note. Similarly, we can proceed by comparing the 4th to 15th pages read yesterday with today's. This would imply that the sum of the numbers of the first three pages read yesterday must be equal to $12 \cdot 12=144$, i.e., the first three pages read yesterday are 47, 48, and 49, and the rest of the solution remains unchanged.

Evaluation. 3 points for any form of the above scheme; 2 points for determining the pages read; 1 point for the result.