PUZZLING PRODUCTS

 

Mindbending Puzzles
101–110

 

 

 

101.  PYRAMID PROBLEM

A pyramid has 16 cubes as its base, with each brick being 16cm in length and 16cm from the bricks next to it. Nine cubes are placed symmetrically on top of this base, four cubes are placed symmetrically on top of these, with finally one cube in the middle on top. In each case, every cube has one-ninth of its base area resting on the four cubes immediately below it. What is the height of the pyramid?

SOLUTION 

 

 

 

102. GRIDLOCK

Using just two different numbers, complete the grid, performing the calculations in order left to right and top to bottom.

SOLUTION

103. CANDLE CONUNDRUM

The two candles shown in the diagram above are made of exactly the same material, and are lit at exactly the same time. They both burn an equal volume of material at the same rate. At what height will they be equal?

SOLUTION

104. HOPSCOTCH

Professor Haggis is devising a
 new game of hopscotch to help
the children with their mathematics. She has almost finished marking
out the grid and has just one
number to chalk in. What should
the number be?

SOLUTION

105. ATTENDANCE RECORD

During the first week of the ice hockey season, the attendance figures from Monday to Friday decreased every day, and on each day, the attendance figure was a palindrome (i.e. read the same backwards as forwards). All of the digits from 0 to 9 appeared, but none of them on more than one day. The smallest attendance of 464 happened on Friday, and the difference between the attendance figures on Monday and Tuesday was 11. The total attendance over the 5 days was 8888. What was the attendance on Thursday?

SOLUTION

106. A PUZZLING SUM

If the first two numbers total 8679, what is the total of the second set of numbers?

SOLUTION

107. TWICE THE FUN

Five brothers all applied for loans of different values. Andy’s loan was $75,000 larger than Brian’s, which was $45,000 less than Jon’s. Jon in turn had been loaned $15,000 more than Eddie, who had borrowed $15,000 more than Dave. The sum of Brian and Eddie’s loans was $120,000. What was the value of the loan taken out by each brother?

SOLUTION

108. MRS. BLOOMER

Mrs. Bloomer has a large number of small pentagonal serving plates that have spaces for five serving portions and a dip in the center. As well as the dip, there are only four different items – carrot slices, cucumber strips, breadsticks and potato chips – to serve and she wishes to ensure that all plates have all four items, but that an item does not appear next to an identical item. How many guests can she entertain at the dinner table if all the plates have a different presentation? (Rotations of plates can be ignored.)

SOLUTION

109. ROPE BRIDGE PROBLEM

Four explorers in the jungle have to cross a rope bridge at midnight. The bridge is only strong enough to support two people at a time. Between them they only have one torch, which they need to be able to cross the bridge. Thomas can cross the bridge in four minutes, his sister Sarah can cross the bridge in seven minutes, their father Charles can cross in 11 minutes, but old Colonel Montmorency can only hobble across in 18 minutes. How quickly is it possible for all four explorers to reach the other side?

SOLUTION

110. RIDING TANDEM

Three brothers have one tandem bicycle. They intend to watch a football match 16 miles away that starts at 3 p.m., and decide to share the walking and cycling. The twins cycle at 12mph alone, and together at 16mph. David cycles at 9mph alone and at 15mph with one of the twins. The twins walk at 5mph. David will not walk at all. At what time should they leave home, allowing five minutes for cycle changeovers and entry into the stadium, assuming they are aiming to arrive in the quickest time possible?

SOLUTION