Puzzle of the Week #28 - Vase (part 2)

This puzzle re-uses the same glass vase from Puzzle of the Week #26. I added an encoded solution in the comments of that question.

I have a glass vase, with a square base and vertical sides. The vase is 50mm x 50mm, and 260mm high. The bottom 10mm is solid glass, and the remaining 250mm has 1mm thick glass walls.

The density of glass is 2.4 times that of water. When I pour a small amount of water into the vase, the centre of gravity is brought down slightly. As more water is added, at a certain point the centre of gravity will begin to creep back up.

How much water added to the vase, to the closest millilitre, will give the lowest centre of gravity for the vase and its contents?

Puzzle of the Week #27 - Dice Logic

Four cube-shaped dice have a different letter on each of their faces, so that between them they feature the first 24 letters of the alphabet, A to X, exactly once each.

I throw the four dice, and make a note of the four uppermost faces. I do this repeatedly, the results of which are shown below. Can you work out what letters are on each of the dice? The letters on one of the dice can be rearranged to form the surname of some famous brothers.

ACDI      BKNW   BHMO   CNSW   CIPQ      CHSU     CGLN     DFRU     DEOR     DHVX    EIMU     FNST      FILO       JMNW QTUV

 

 

Puzzle of the Week #23 - SE Words

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

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


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?