PUZZLING PRODUCTS

 

Mindbending Puzzles
111–120

 

 

 

111.  CROSS NUMBER

Insert the missing numbers into the grid so that all calculations are correct reading both across and down. All numbers to be inserted are less than 10.

SOLUTION

 

 

 

112. CATS AND DOGS

In the village of Hambledown
70% of the houses had at least one cat and 60% had at least one dog. There were 20 houses without any pets and 80 houses with at least one cat and at least one dog. How many houses were there in the village?

SOLUTION

113. LETTER LINK

In the diagram, each letter represents one of the numbers 0 to 9, added together to give the totals shown. Can you work out how much LAGOON is worth?

SOLUTION

114. FUN RUN

Harvey recently took part in the annual fun run for the guards of Laguna. All managed to complete the course and Harvey was positioned somewhere in the top half. It was noted that if 10 more guards had finished in front of
him rather than behind him he would have been first in the
bottom half. However, if six of
those in front of him had finished behind him he would have just crept into the top 10%. How many guards took part in the run and where did Harvey finish?

SOLUTION

115. PIECE OF CAKE

Flora is baking cakes. She’s set herself a challenge to ice the cakes with the numbers 1 to 9, and arrange them in a line such that:
numbers 1 and 2 and all the
digits between them add up to 21;
numbers 2 and 3 and all the
digits between them add up to 12;
numbers 3 and 4 and all the
digits between them add up to 24;
numbers 4 and 5 and all the digits
between them add up to 25.
(The numbers do not have to appear in ascending order.)

SOLUTION

116. A PUZZLING SUM

Laura teaches mathematics to young children in the morning and teenagers in the evening. She puts five different numbers on the board and asks the youngsters to add together any three. She puts these answers on the board, and removes the five original numbers. In the evening she asks the teenagers to work out what the original numbers were. One bright student states that there are ten different ways to add together any three of five numbers, but that there are only nine on the board. Laura confirms that all the possible numbers are included. What were the original five numbers?

SOLUTION

117. HALF MEASURES

Draw just one line to divide the circle into two equal halves so that the numbers in each half add up to the same total.

SOLUTION

118. MAGIC SQUARES

Here are two incomplete magic number squares in which only some of the horizontal, vertical and diagonal lines total 65. However, by swapping just three numbers in the left-hand square with three numbers in the right-hand square it is possible to create two magic squares where all lines total 65.

SOLUTION

119. POSTAL PROBLEM

The Laguna postal service only accepts parcels that have at least one square side. What is more, when measured in inches, if the volume (X cubic inches) is the same as the total surface area (X square inches) no charge at all is made for postage. There are four parcel sizes that fit this bill: three are 6x6x6,
5x5x10 and 8x8x4. Can you find the other one that has a value for X of 432?

SOLUTION

120. MECHANICAL MAYHEM

An industrial machine has four
cogs that are meshed together.
The largest cog has 15 teeth, the next 14 teeth, the next 13 teeth and the smallest has 12 teeth. How many revolutions must the largest cog make before all cogs return to their original positions?

SOLUTION