3

Part of 2014 Tournament of Towns.

Problems(2)

TOT 2014 Spring O J3, numbers on a 7x5 table

Source:

The entries of a

7 \times 5

table are filled with numbers so that in each

2 \times 3

rectangle (vertical or horizontal) the sum of numbers is

0

100

dollars Peter may choose any single entry and learn the number in it. What is the least amount of dollars he should spend in order to learn the total sum of numbers in the table for sure?

combinatoricstable

TOT 2014 Spring A J3, areas with intersecting squares

Source:

A square table is covered with a square cloth (may be of a different size) without folds and wrinkles. All corners of the table are left uncovered and all four hanging parts are triangular. Given that two adjacent hanging parts are equal prove that two other parts are also equal.

geometrysquareareas