Puzzle of the Week #300 - Winner Stays On

Four friends, Alfie, Billie, Charlie and Debbie, play a series of games on their pool table. At each point, two of the friends are playing each other while the other two are reduced to spectating. After each game, the winner stays at the table and will go on to play whichever of the two spectators has been waiting the longest since their last game, and the loser becomes a spectator for the next game, in order to ensure everybody gets to play.

 

After they have finished Alfie has played in eight of the games, Billie three, Charlie six and Debbie five.

 

Who lost in the ninth game?

Puzzle of the Week #299 - Change a Letter

Change one letter from each word, and THEN re-space to form an aphorism:

 

For example:

TO  YOGA  INFO  ILL  GRIN  FAN  LIE  TIER

becomes:

TR  YAGA  INFA  ILA  GAIN  FAI  LBE  TTER

then:

TRY AGAIN FAIL AGAIN FAIL BETTER

 

 

CHEF  CAME  TO  IT  BUT  NOT  WISE  AT  BRAG  AT  OUR  ASH  AS  FAST  ONE

Puzzle of the Week #298 - Unit Fractions

It is well known that if you add together all of the unit fractions, 1 + 1/2 + 1/3 + 1/4 + 1/5 + … all the way to infinity, the answer is also infinity (although it approaches it ridiculously slowly).

However, if we throw out any that have a never-ending decimal, such as 1/3 (0.333…), 1/6 (0.166…) ,1/7 (0.142857…) etc, and only include those that have a terminating decimal expansion:

S = 1 + 1/2 (0.5) + 1/4 (0.25) + 1/5 (0.2) +1/8 (0.125) + 1/10 (0.1)… all the way to infinity,

we do get an actual number as the result. What is it?


Puzzle of the Week #295 - Base 4 Code

I have taken a quotation, and I have replaced each of the letters with the numbers that denote their position in the alphabet. However, I have used the base 4 number system. 

Be careful, as some sequences of numbers could lead to several words, for instance 31110 could mean CAT (3,1,110), but could equally mean MAD (31,1,10). 

base4.JPG

11020213213103  1133310223  33111110  211103110  1233102  110203310311  1132033  3112311  1102011  211103110  3312  1102011  1131121  11020213213103  1133310223  33111110.

22332032  1133333101132.

Puzzle of the Week #294 - Special K

K, L and M are all positive whole numbers.

For the certain special values of K that we seek, the same values of L and M that cause (KxL)+(4xM) to be a multiple of 11 also cause (KxM)+(5xL) to be a multiple of 11.

For instance, K ISN’T 2, because some values of L and M that make (2xM)+(5xL) a multiple of 11 (eg L=1,M=3) when you plug those same values of L and M into (2xL)+(4xM) give a number that is NOT a multiple of 11 (in this case 14).

Out of the possible values of K for which the divisibility by 11 of (KxL)+(4xM) and (KxM)+(5xL) are always in agreement, what number is the THIRD LOWEST PRIME?


Puzzle of the Week #292 - Base 4 Code

I have taken some quotations, and I have replaced each of the letters with the numbers that denote their position in the alphabet. However, I have used the base 4 number system. 

Be careful, as some sequences of numbers could lead to several words, for instance 31110 could mean CAT (3,1,110), but could equally mean MAD (31,1,10). 

base4.JPG

12133111  3132  1112332110  1021113021110121,  2111110  12133111  3132'110  1112332110  1102011  33332103111011111132311103  3312  1112332110213213  1021113021110121. 

Puzzle of the Week #290 - Special Sequence

This is a special sequence:

3 1 2 1 3 2

For each number ‘k’ from 1 to 3, the number of numbers between the pair of ‘k’s is equal to k.

In other words, there is one number between the pair of 1s, two numbers between the pair of 2s and three numbers between the pair of 3s.

Can you create a similar sequence containing pairs of numbers but using numbers 4, 5, 6 etc up to n (n can be whatever you need it to be to make a sequence that has no gaps), where for each number k, the number of numbers between the pair of ‘k’s is k (so there will be four numbers between the pairs of 4s, five numbers between the pair of 5s, etc.)?

 

 

Puzzle of the Week #288 - Round Table

A family that consists of parents and 6 children sit around a table in age order: father, mother, eldest child etc, so the youngest child sits next to the father.

The gender of each of the children is male or female, with 50% probability of each.

Knowing only this information, what is the probability that all the males are seated together?


Puzzle of the Week #286 - The Cube and the Cup

This came to me whilst trying to balance a Rubik’s cube on the circular rim of a coffee cup. There are three ways of orienting a cube on top of a cup, which I’ll refer to as face-down, edge-down (resting on the rim in four places) and point-down (resting on the rim in three places. For these latter two cases the cube extends below the level of the rim of the cup. Depending upon the particular cube and the particular cup, the cube might extend deeper into the cup when it is edge-down or when it is point-down.

cubes.jpg

Assuming that the edge-down and point-down orientations are possible for the given cube and cup, how can you tell, very quickly and without using any measuring devices, only looking at and manipulating the cube and the cup, which of those two orientations extends deeper into the cup?

Puzzle of the Week #285 - Left Right Pairs

This puzzle was inspired by a real-life problem I had in my job as an engineer. Faced with a number of lengths I needed to come up with a set of left parts and a set of right parts which could combine to form every length on the list. For instance, the length 52 could be made up of 26L + 26R, or 20L + 32R, or any number of different combinations. For reasons of making and stocking the individual left and right parts it was important to minimise the total number of different parts I needed.

For this puzzle I have massively shortened and simplified the list but the idea remains the same: what is the least number of distinct parts you will need, some left-handed, some right-handed (parts that are the same length but different hands count as two different parts), that will fit together in left-right pairs to form any length on this list:

20 23 28 44 46 48 50 52 56 58 70 74