Structural aspects of the Indiscreet Fortune Teller game with six columns

Abstract

This article aims to present the game Adivinho Indiscreto with six columns, highlighting its structure and didactic potential for Mathematics teaching. The game can be used as a didactic strategy for addressing topics such as exponentiation and the Binary Number System, providing a playful and stimulating learning environment. In it, the participant mentally chooses a number between 1 and 63 and indicates in which columns the number appears; from this information, the instructor can correctly identify the chosen number using logic based on the sum of powers of 2. The analysis, carried out through a Qualitative and Exploratory methodology, reveals that each number from 1 to 63 can be represented as a sum of powers of 2 with coefficients 0 or 1, corresponding to its binary representation. The limitation of the range from 1 to 63 is directly related to the number of columns (six) and the 64 possible combinations of binary coefficients for powers of 2 with exponents from 0 to 5. The only discarded combination is the one in which all coefficients are 0, which would represent the number 0 — not included in the game. It is concluded that Adivinho Indiscreto is a didactic strategy with the potential to enrich mathematics teaching and learning at different educational levels, as well as enabling further investigations and adaptations in the construction of Adivinhos Indiscretos with different numbers of columns other than six; explorations of why the first column (from left to right) of the game contains all odd numbers between 1 and 63; and other possible mathematical organizations that may relate to the game.