Puzzle of the Week #422 - Boggle E

Find all of these common words within this Boggle grid, each containing the letter E.

Each letter after the first must be a horizontal, vertical, or diagonal neighbor of the one before it.

No individual letter cube may be used more than once in a word.

B - - - E

B E - -

B E - -

C - - E

C - - E

C - - - - - E -

D E - -

D E - -

F - - E

F - - E -

F - - E

G E - - -

H E - -

H E - -

L - E -

L - - E

M - - E

 

 

 

Puzzle of the Week #421 - Odd Prime Balance

I thought about throwing you in the deep end on this one, but even just the last part of the puzzle is challenging enough, so I’ll lead you up to that point:

We saw from the Prime Balance puzzle (POTW #380) that if we want a number of distinct prime number blocks equally spaced around a circle to have a centre of gravity at the centre of the circle, the least number of blocks is six. This is because if you want distinct rational weights, the number of weights cannot be a prime or a prime power. If we add in a further stipulation that the number of blocks must be odd, the lowest number that is odd but neither a prime nor a prime power is 15.

Using the fact that 15 is 3 x 5 we can set up a system of equations as we did before:

 

A = V

B = W+T

C = X+U

D = Y

E = Z+T

F = V+U

G = W

H = X+T

I = Y+U

J = Z

K = V+T

L = W+U

M = X

N = Y+T

O = Z+U

 

Whatever we choose for T to Z the system of blocks will be balanced around the centre of the circle. We still have to ensure that the numbers A to O are all prime and all different. What is the least possible total weight of the 15 blocks?

 

Puzzle of the Week #419 - Minimum Triangle

This right-angled triangle is shown with its inscribed circle (incircle). The distances a and b make up the distance from each end of the base to the tangent point of the incircle. c is the height of the triangle, perpendicular to the base.

If I tell you that a, b and c are all whole numbers, and all different, what is the minimum sum of a, b and c?

Puzzle of the Week #418 - Fourth Circle

Three circles of radius 70, 20 and 50 are mutually tangent.

A fourth circle is introduced, which passes through the centre of the 50 circle, and which is also tangent to both the 20 circle and the 70 circle at the point that they are tangent to one another.

What is the radius of this fourth circle?

Puzzle of the Week #417 - Triple Duality

The answer to each clue is a 3-, 6-, or 9-letter word. If you split these into 3-letter chunks, you will find 20 different ‘triples’ each appearing twice.

For example if one answer was ‘bellow’ then ‘bel’ and ‘low’ would appear somewhere else too, for instance in ‘disbelief’ and ‘lowest’, but then ‘dis’, ‘ief’ and ‘est’ would have to appear somewhere else too, etc, until all triples have appeared exactly twice.

 

Age

Be present at

Christian religious leader

Condensed water droplets

Endurable

Finish

Imperfections

'In the name of Allah'

Mold

Opinion, recommendation

Outcast

Part of a circle

Part of speech

Part of triple jump

Set upon

Shiite religious leader

Softcover

Suitable for purpose

Tropical fruit

Underneath the ...

Vanilla ..., rapper

 

Puzzle of the Week #415 - Alchemy

You can change one word into another of the same length by a series of steps whereby at each step you change one of the letters and rearrange to form a valid word. This differs from usual word ladders where you aren’t permitted to rearrange the letters.

LEAD and GOLD both contain L and D so would only require two steps to change between them, so just one intermediate word, for instance: LEAD – GLAD – GOLD.

Can you change CARBON into SILVER in only five steps (four intermediate words)?

Puzzle of the Week #411 - Best Remakes

Watching the Oscars this year I noticed that one of the nominees for Best Picture was a remake of one of the very first winners almost a century ago. In fact, in four of the last five years, a Best Picture nominee has been a remake of a film to previously be nominated for Best Picture. I trawled the lists and found several more examples for you to try and discover below. Where a film has three or more words in the title, I’ve given the initials; where it has only a single or two-word title, I’ve given an anagram.

 

Winner 1930, nominated 2022: AQOTWF

Winner 1961, nominated 2021: WSS

Nominated 1933 and 2019: TIME NOT WELL

Nominated 1937 and 2018: ASIB

Nominated 1935 and 2012: SMELLIER BASES

Nominated 1952 and 2001: GERONIMO ULU

Nominated 1943 and 1978: HCW

Nominated 1936 and 1968: RAJ

Nominated 1934 and 1963: ACE PATROL

Winner 1935, nominated 1962: MOTB

Puzzle of the Week #410 - Six Starfish

Enter the letters E, N, I, G, M and A into the circles at the end of the starfish tentacles, so that: 

Each starfish will have each letter once each. 

Each straight line (indicated by an arrow) will have each letter once each. 

Each triangle (indicated by a bold line) will be surrounded by each letter once each. 

Puzzle of the Week #409 - Classes

A school year is split into three equal classes. Every student either is either a boy or a girl, with the total number of boys and girls being equal.

 

Class A has twice as many girls as class B, and four times as many boys as class C.

Class C has two more girls than class B has boys.

 

How many students are there altogether?

Puzzle of the Week #406 - Strange Area

I have a shape as below: a concave pentagon. Two of the points are the ends of the base of a unit semicircle. Two other points lie on the semicircle; at those points the angles are right angles. Four of the five edges are equal in length, and the fifth length (being the base of the semicircle) is equal to 2.

What is the area of the pentagon?