The number system is considered to be one of the most innovative and exciting inventions by human beings. Using number system concepts, experts have invented various tricks and puzzles involving numbers. These puzzles make a student curious and boost his/her will to study. These puzzles are not only for fun, but it also enhances the thinking process of students, thus turning maths easy for them. The objective of introducing puzzles in maths is to test the knowledge, intelligence and thinking ability of students and how much they are clear on the different concepts of mathematics. In this article, we have some tricky maths puzzles with answers that will help a student to enhance his/her knowledge.
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In order to solve number puzzles, it is necessary that a student should have some knowledge of the number system. Without any knowledge on the number system, it is impossible to solve maths number puzzles. In this article, you will also get an overview of the number system along with simple math puzzles.
A number system is considered to be a system of writing that expresses different numbers. The number system is considered as a mathematical notation used to represent numbers of a given set with the use of digits and other symbols in a consistent manner. A number system is responsible for providing a unique representation of every number and also represents the algebraic and arithmetic structure of various figures. Number system allows a student to use arithmetic operations like addition, subtraction and division.
The value of any digit can get determined by:
Its position in the number.
The base of the number system.
In mathematics, there are various types of number systems, among which the four most common ones are:
Decimal number systems have base 10 because this type of number systems uses ten digits which starts from 0 to 9. In the decimal number system, the positions that are present successive to the left of the decimal point represent units, tens and so on. Due to this, the system is always expressed in decimal numbers.
The number system which has a base 2 is known as a binary number system. In this case, only two binary digits exist, which are 0 and 1. The usual base 2 is considered as a radix of 2. Figures that are mentioned under this binary system are termed as binary numbers which are a combination of 0 and 1.
The number system which has a base 8 is known as an octal number system. In this case, the number system uses 8 numbers that are from 0 to 7. Octal numbers are mainly used in computer applications. Conversion of an octal number into decimal is similar to the decimal conversion.
In the hexadecimal number system, numbers are written and represented with 16 as a base. In this number system, the numbers are first represented in the same way as the decimal number system, and after that, they are represented as alphabets from A to F.
In a puzzle, each letter represents only one digit which means that one letter stands for one digit.
In the case of puzzles, the first digit of a number can never be zero. For example, students write sixty-six as 66 and not as 066.
1. Find the value of Q from the following
4 Q 1
3 8 Q
8 0 3
In column one (starting from the right), from Q + 1, we get 3 at the units place.
⇒ Q + 1 = 3
⇒ Q = 2
In the middle column,
Q + 8 gives a number in such a way that it has 0 at its units place. So Q = 2. This is verified by the fact that when Q that is 2 is added to 8, it results in 10 and hence 1 is carried forward. In the third column, the result will be 4+3+1 = 8 ( 1 is carried).
2. Find the value of A:
A is a number whose thrice sum of itself also results in A. Therefore, A + A = 0. This case is possible only when A = 0 or A = 5.
In this case if A = 0,
The entire sum will be 0
Thus, B = 0.
This will lead to A = B which is not possible.
We know that different letters represent different digits. Therefore we have to consider the case in which A = 5.
Hence 5 + 5 + 5 = 15
Therefore, B = 1.
Q1. How do You Introduce a Number System?
Ans: Number system makes the use of different number bases to classify different number systems into categories. A number base is considered to know the number of digits that are available when a particular number system is used. For example, the number system with base 10 uses the digits that are between 0 to 9. This is what the number system is in real life. In the above article, mathematical puzzles with answers help students to understand the number system more clearly, thus making their preparation for the exams more efficient and productive. Students with good knowledge of the number system can secure good marks in math exams.
Q2. Why are Puzzles Used in Mathematics?
Ans: Mathematics is one of the hardest subjects that a student has to face in his/her academics. Many students find this subject hard; thus, they don't get curious to learn more in mathematics. They consider this subject boring. Hence, puzzles are introduced in mathematics for attracting students and get them more involved in mathematics. They become more curious to solve these problems. This solving exercise expands their knowledge of mathematics, and they become more skilful. Students find mathematics interesting despite being bored after the introduction of these puzzles in mathematics.