Maths Puzzles

In 2024, most of the world is either excited or anxious about elections, let us talk about elections.    At a recent small town election for mayor a total of 963 votes were cast for the four candidates, the winner exceding his opponents by 53, 79 and 105 votes, respectively. How many votes were cast for each candidate?  

Now here is a question simple enough to solve. Solution : Let us say there are x children, y women and z men. y = 2x x = 2z y = 2 (2z) = 4z And x+y+z = 35 Substituting each of x,y,z in terms of z, we get 2z + 4z+z = 35 7z = 35 z = 5  There are 5 men. x = 2z = 10. There are 10 children y = 2x = 20. There are 20 women So in there party, there are 5 men, 20 women and 10 children.

 Here is the solution to puzzle 83. Let us say Gordon's current age is x and Tony's age is y. x+y = 112 y = 112-x When Gordon was y years old, Tony was y - (x-y). (As the age difference will remain the same) But now Gordon is twice as old as this age -  x = 2(2y-x) 3x -4y = 0 4x+4y = 112*4 7x = 112*4 x = 112*4/7 = 64 y = 112 - 64 = 48 Gordon is 64 years old and Tony is 48.

I know you have read such  age puzzles a million times. Now I will tell you million one-th puzzle. But as a repentance,  I am giving out a simple trick to find the square of smaller numbers. With an example.    Let us say you want to find the square of 37. Which is the nearest number you know  the square of? 30? OK. 30 is 7 below 37. Take a number 7 above 37 too - 44. Now multiply 30 and 44. You get 1320 right. Now square the number 7 - the one you have used to go above and below the number. You get 49. Add this square to 1320. 1320+49 = 1369. Isn't that the square of 37 - find out with your calculator app.  Use this trick to find the square of 43.  43 -3 = 40.  43+3=46.   40X46 = 1960 3 2 is 9. Add this to previous product. 1960+9 The answer is 1969 - square of 43 is 1969

 Five children share some sweets equally. They eat 8 sweets and save some for later. The number of sweets left together is equal to the number of sweets each child received in the beginning.  How many sweets did each child receive?   Solution: Let us say each child received x sweets.  And each child saved y sweets.  So total number of sweets saved by all children = 5 *(x-8) But this number is equal to the number of sweets received by each child. So x  =  5(x-8) x = 5x-40 40 = 4x x  = 10 Each child received 10 sweets.   

 This was the  puzzle Let us say I spent b rupees on bag, s1 rupees on saree and s2 rupees on shoes. Total amount = 1400 = b+s1+s2   -----(1) s1 = 900+b -- as saree cost 900 more than bag s1 +b  = s2+1200 --- (2)      as saree and bag cost 1200 more than shoes.  b = s1-900. Substituting b in the first equation, we get   1400 = 900+b+b+s2 500 = 2b+s2 --------(3) Substituting s1 = b+900 in equation 2, we get b+900+b =s2+1200 300  = 2b-s2 ---------(4) Adding 3 and 4 we get 800 = 4b b = 800/4 = 200 s1 = b+900 = 1100 s2 = 1400 - s1 - b = 100   Saree cost rupees 1100, shoes cost rupees 100 and bag cost rupees 200. 

This was puzzle 80 about fruit baskets.   Let us say the fruit seller sold x large baskets and y small baskets. But x= y, as he tells he sold equal number of large and small baskets. In large baskets he sold 12 pears each = 12*x pears In small baskets he sold 5 pears each = 5*x pears Total pears he sold = 68  12x+5x = 68  17x = 68 x = 68/17 = 4 He sold 4 large baskets of 12 pears and 4 small baskets of 5 pears.

 Here is the solution to puzzle 81 The running track he took is in elliptical shape. The circumference or perimeter of an ellipse can be approximated as π √ (2 (a 2 +b 2 )) where a is semi-major axis and b is semi-minor axis. So in our example, a is 200/2 = 100 and b is 50/2 = 25 So circumference = 22/7 *  √ 2 *  (100 2 +25 2 ) = 22/7 *  √ 2 *  (10000+625) =458.15 m. So Jenny is correct.

The diagram shows a rectangular field with a length of 200m and a width of 50m. Billy runs around the oval track shown, making contact with the fences of the field four times. Billy says that he has run more than 500m but less than 600m. Jenny says that he has run more than 400m but less than 500m. Maggie says that he has run more than 300m but less than 400m. Who is correct?

  A fruit dealer packages pears in two different box sizes. One size holds 5 pears and the other size holds 12 pears. The dealer sold 68 pears in one of the stores in one hour. He said to his assistant, “You don’t see that very often. We sold the same number of boxes of each type of packaging.” How many boxes of each size did they sell in one hour?

 

 Here is the solution to puzzle 78 Solution: Let us say her age now is x. So 3 years later her age is x+3. 3 times that is 3x+9. Her age 3 years ago is x-3. 3 times that is 3x-9 When you subtract them, you get 3x+9 - (3x-9) = 18. She says that is her age. Her age is 18.