Mathematics is not only about mechanically doing sums and to solve math problems, but training the mind to think critically. In a mathematics class, one needs to encourage and motivate students to think “out of the box” and **Help With Math Problems** to get rid of the fear of “numbers”; the classes need to be interactive where students should be asked to explain how they would solve a particular problem. Few interesting maths puzzles are given below for inquisitive minds:

**Puzzle 1:**

In the adjoining addition sum, P, Q & T are 3 distinct non-zero digits. Find their values.

## Puzzle 2:

Find the positive integral values of x, y, z such that 29x + 30y + 31z = 366.

## Puzzle 3:

From the following conversations find the respective ages of 3 children (it is given that ages are in integers).

Mr.X : I know you have got 3 sons . What are their ages? Mr.Y : The product of their ages is 36. Mr.X : Give me some more information. Mr.Y : The sum of their ages is my house number which you definitely know. Mr.X : Yes ,I know but give me some more information. Mr.Y : My eldest son is an outstanding singer. Mr.X : Thank you so much. Their ages are _______, ________ & _________.

# Solutions:

## Puzzle 1:

⇒ 10P + Q < 100

and 10Q + P < 100

⇒ 11P + 11Q < 200

So, T = 1 & the sum must be divisible by 11.

i.e. TPT must be 121.

Hence, Q = 9 & P = 2.

## Puzzle 2:

Think about a leap year which has 366 days; Feb has 29 days; there are some months with 30 days and others with 31 days.

This will allow you to determine x, y and z

## Puzzle 3:

Product of the ages = 36

Possible factors |
Sum of Factors |

36 X 1 X 1 | 38 |

18 X 2 X 1 | 21 |

12 X 3 X 1 | 16 |

9 X 4 X 1 | 14 |

9 X 2 X 2 | 13 |

6 X 6 X 1 | 13 |

6 X 3 X 2 | 11 |

4 X 3 X 3 | 10 |

Only when the sum is 13 there are 2 possibilities and that is why Mr.X Could not answer. Hence the apparent useless information “Eldest son is an outstanding singer.” will be the last information as it indicates that the eldest son is unique. So it cannot be 6 X 6 X 1 . Therefore, their respective ages will be 9, 2 & 2.

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