Puzzle of the Week #18 - Egyptian Fractions

In ancient Egypt, they only liked to use so-called unit fractions, which are fractions that have 1 as the numerator. If they wanted to represent a fraction that wasn't already a unit fraction, they would express as the sum of different unit fractions.

So, for instance 3/4 = 1/2 + 1/4. and 2/7 = 1/4 + 1/28.

How can you express 39/50 as a sum of different unit fractions?

Puzzle of the Week #17 - Quotebreaker

Quotebreaker is back by popular demand! 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).

213210313211 10011331003011 110211 1301131121103 10311110211 110201110 1102011121 110211 12213211. 21110 21103 333230121 1102011 10313211 10011331003011 1132033 110211 113213030213213 11033 1103121110 110201110 1102011121 110211 31021122121.


Puzzle of the Week #15 - Bolt Head

I’ve used a micrometer to measure a bolt head, both from edge to edge, and from point to point.

I later realise that I had forgotten to ‘zero’ the micrometer before I used it, meaning that both measurements are wrong, but they are wrong by the same amount.

What should the measurements be?

Puzzle of the Week #14 - NE Words

Can you think of five four-letter words, each beginning with NE?

Sounds simple, however you cannot use a letter more than once, and you can’t re-use the N or the E anywhere else. So for instance, NELL is not allowed, as it has two Ls, NEON is not allowed as it repeats the N, and you cannot have both NETS and NEAT, as both have a T, but either word is acceptable on its own.

Puzzle of the Week #13 - Sloping Wall

I've built a sloping wall, on level ground. One end is 10ft high, and the other end is 15ft high.

I attach a piece of string from each top corner to the opposite bottom corner, forming an 'X' shape. Assuming the strings are pulled tight, what height from the floor is the point where the two string cross?

Puzzle of the Week #9 - Third Avenue

Draw a path that visits every dot once only.

The path can be made only of horizontal and vertical lines.

The path cannot cross itself or branch off, and must return to the start to form a complete circuit.

Every third turning point of the path has been marked with a triangle symbol. In other words, at each symbol there will be a 90 degree turn in the path, and there will be two further 90 degree turns before the next symbol.

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Puzzle of the Week #8 - Quotebreaker

Quotebreaker is back by popular demand! 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).

233121103  113213030  211  233121103,  13210  10333  113213030  1  3033110  3312  312110103011-1131110  311132.

Puzzle of the Week #6 - Paddocks

Draw fences between some of the posts so that each post is at the junction of exactly three fences.

These fences will divide the field into several paddocks; any paddock whose area is greater than a single triangle will contain a number, which will indicate the area of the paddock that contains it.

The boundary fence is already in place, so any post on the boundary only needs one more fence emerging from it in order to make up its full complement.

For example:

Here is the puzzle:

Puzzle of the Week #3 - Shaded Squares

I have shaded some squares in the left-hand grid according to two simple rules:

Rule 1 – Squares that are next to each other, horizontally or vertically, cannot both be shaded.

Rule 2 – All the unshaded squares must be connected. In other words, you must be able to get from any unshaded square to any other unshaded square by moving horizontally or vertically through unshaded squares.

I have shaded 11 squares in the left-hand grid, but I can’t shade a 12th square without breaking the rules. For instance, shading the ‘E’ square would break rule 1, and shading the ‘3’ square would break rule 2 (as the ‘6’ and ‘8’ squares would be separated from the other unshaded squares).

However, if you start again, it is possible to shade 12 squares without breaking the rules. I have shaded two squares in the right-hand grid to start you off.

Which squares should you shade? 

Puzzle of the Week #2 - 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).

2112  1110  1221102103110  12133111  103332'110  10311133111110,  313030  10110!

Puzzle of the Week #1 - Strange Stamps

The islanders of Fictitia have a rather eccentric postal system. Postage for an item can be anything from 1 dinar to 12 dinari, and you must use exact postage.

Frustratingly, there is only space on the envelopes in Fictitia to attach a maximum of two stamps.

What is more, they only have four different denominations of stamps, can you work out what they are?