Puzzle of the Week #49 - Pair-of-Dice Regained

I have a pair of dice, which are numbered in an unconventional way. Unlike normal dice, where you can achieve a maximum total of 12, and often the same total can be achieved in several different ways, (eg 5+2=3+4=1+6=7, etc), these dice can total any number from 2 to 37 in exactly one way each.

All of the numbers on the dice are positive whole numbers, and one of the dice has four square numbers on it.

How are the dice numbered?

Puzzle of the Week #46 - Pros and Cons

Below is a grid which you will need to fill with ten pairs of common words that differ only in that the first three letters of each word are ‘pro’ or ‘con’ (for example, ‘productivity’ and ‘conductivity’).

I have encoded all of the other letters as numbers.

Can you fill in the grid?

Puzzle of the Week #45 - Three Dice

I have three special dice. They are each 6-sided, and each has a positive whole number on each face.

Unlike standard dice, where the highest number achievable is 18, and many numbers can be achieved in several different ways, these special dice can total any whole number from 3 to 218.

The numbers on the first die total 174. The numbers on the second die total 348.

Level 1 challenge: what is the total of the numbers on the third die?

Level 2 challenge (for super-humans only): what numbers are on each of the dice?

Puzzle of the Week #44 - Step by Step

The answer to each of these clues is a five letter word. To get from each answer to the next, you replace one letter and then rearrange. For example if one answer was TRIAL, the next could be LATER. There is a link between the first and last answers.

League standings

Turning machine

Swindle

Arrive at

Preside over a meeting

 

Puzzle of the Week #43 - Hypothesis

You have in front of you five cards that are coloured on both sides. The five visible faces are red, blue, green, yellow and orange.

You are given a statement that:

‘If a card has red on one side it must have either blue or yellow on the other side’

You decide to turn over some of the cards in order to discover whether this statement is true or false. Which cards do you need to turn over?

Puzzle of the Week #42 - TriBall

TriBall is a sport which is played between two teams of three players.

My local TriBall club has an annual tournament.

In the tournament, every possible trio plays every other possible trio exactly once each. Luckily the ‘matches’ are only a couple of minutes in length, but even so the tournament takes a while to complete.

The club has one more member this year than it did last year. As a result, the total number of matches in the tournament is exactly three times as many as last year.

How many members are there in my TriBall club?

 

Puzzle of the Week #40 - Pyramid

And Lo! He did build a pyramid, and the base was a perfect square with area between one third and two thirds of an acre*. The length of each side of the square was an exact whole number of yards. The height of the pyramid was a prime number of yards, as was the distance from each corner to the apex.

What were the dimensions of the pyramid?

(* An acre is an area of 4840 square yards)

 

Puzzle of the Week #39 - Quotebreaker

I have taken a quotation, and I have replaced each of the letters with one-, two- of three-digit numbers according to the table below. Can you change it back to letters?

Be careful though, 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).

31021111102111221110121 10211100102111031132110103 1 3121102131113033111103 33331213213 1103313111102011102 3312 1102011 11132213220212211101110 11321110213121 3312 1102011 320213010 1132111020 21110103 110010011021132110 33100100331032111011 13210 11321131121, 1102011 103113210311 3312 331021011102 2131100331031110 3332 1102011 10211033211003021321110 11011130110 213211011303021131132311.


Puzzle of the Week #38 - Palindromic Numbers

Some numbers are palindromic (reading the same backwards as forwards), such as 242, 12321 of 55.

38 is not a palindrome, or at least it isn’t when expressed in base 10.

However it is also a palindrome in three other bases (not including bases above base 38, where the number would be a single ‘digit’).

Can you find all three of them?

Some background on bases: we use base 10 all of the time, and we understand well how it works: each digit moving from right to left is worth 10 more than the last. Other bases work in exactly the same way, but with the digits increasing in value by a different factor. For example, 38 expressed in base 6 would be 102, since (62)x1 + (61)x0 + (60)x2 is equal to 38.

 

Puzzle of the Week #37 - Numbers Game

Using each of the numbers:

11           12           13           14           15           16

and only using basic arithmetic, it is possible to achieve the total of 987:

16 – 11 = 5

5 x 15 x 13 = 975

975 + 12 = 987

This method uses each of the numbers except for the 14.

There is a way to achieve the total of 987 by using all of the numbers once each. Can you find it?

 

Puzzle of the Week #36 - Double Elimination

To celebrate a new parkrun starting in Stratford-upon-Avon on Saturday, this week’s puzzle has a Shakespearean theme.

For each of the following, delete two letters from each word, and then re-space to give the name of a Shakespeare play.

For example CHARM LESS TEA = *HA*M LE** T** = HAMLET

1: JUMP LION UNSCARE SCARE

2: NASTY GHOUL SICK EDITS

3: JOKING CLEAN CAR

4: GIANT CORNY BRAN DISC LEMON PLAIT WRAP

5: TAP TIMID SOUR MIME EARNING THE TEAS DARED ARMY

6: HENCE GORY VIPER ARCTIC MINI

7: THE AIR FOILS MUST STAND CARESS ASIDE AIR

 

 

 

Puzzle of the Week #35 - Odd Word Out

What is the odd word in this list and why?

SEEK
BUY
TEACH
FIGHT

Notoriously, with odd-one-out questions, you will probably be able to find a reason why each of the words in turn should be the odd one. However, the true solution will be both convincing and satisfying, with even my choice of the odd word serving to support your hypothesis. Good luck!

 

Puzzle of the Week #33 - Cryptic Quiz

I am a fan of the BBC Radio 4 show Round Britain Quiz. I have written a question in the style of the show:

Delve beneath the surface and you’ll find the following several leagues below:

300 sprightly sounding Greeks

The Blue Boy, his father and a ghost

Urban arboreal grey matter

And a handcart

What are they?

Puzzle of the Week #31 - Engine Failure

This is an excerpt from my first book, Very Clever Puzzle Compendium: http://www.lulu.com/spotlight/maxelkat

Orville and Wilbur are model aeroplane enthusiasts.

Orville: These new engines you bought are terrible – they keep breaking down in mid air.

Wilbur: I know! That’s why I’ve fitted my new plane with two engines, and as long as at least one of them is still working, it will continue to fly.

Orville: I’ve gone even better: I’ve fitted mine with four engines, and as long as at least two of them are still working, my plane will stay up.

Wilbur: That’s not necessarily better – it depends on exactly what the probability is of each of the engines failing.

Orville: How do you mean?

Wilbur: Well, for instance, if the individual engines break a quarter of the time, the chance of your plane falling from the sky just over five percent, and mine would fail just over six percent of the time.

Orville: So mine would be better!

Wilbur: Yes, but what if the engines break down exactly half of the time? My plane would come down a quarter of the time, and yours would crash just over thirty-one percent of the time – so mine would be better!

 

As it turned out the probability of each of the engines malfunctioning was a magic figure somewhere between one quarter and one half, where the probability of Wilbur’s two-engine plane and the probability of Orville’s four-engine plane crashing was exactly identical.

What was the probability of each engine failing?