The Critical Line – Volume 36

For your chance to win a $50 book voucher, send your solutions to by 5pm AEST Friday 30 July.

A Vaccination Situation

Sydney’s Loch and Downe Enterprises are developing a vaccine to combat a recent virus outbreak. The firm owns a quarantine facility and has recruited 51 volunteers to participate in a vaccine testing program. Volunteers are allocated to individual rooms. The facility is three storeys high with each floor layout as given below:

  • Ground floor: 6×6 rooms including a reception (R) and stairs (S) to level one

  • Level one: 4×4 rooms including the stairs (S) to ground, and a lift (L) to level two

  • Level two: 2×2 rooms including lift (L) back to level one


Note: These images are not directly editable


The vaccine is administered over two doses (A and B) for full effect. You are given the task of administering these vaccines to all volunteers in the facility. The chief medical officer has given you the following instructions:

  • You must start and finish at the reception; 

  • All volunteers must receive vaccine A before any receive vaccine B;

  • Once a vaccine (A or B) is administered to a volunteer and you have exited the room, the room must be sealed off until all other vaccines of that type are administered; 

  • There are doors between each volunteer’s room. Doors to reception, stairs and lift are given; 

  • Once the lift (L) is entered, it will immediately travel up/down, the exit door of your choosing will open and the volunteer adjacent must be treated; and

  •  Volunteer X can only receive vaccine A, as they are allergic to vaccine B

Part A:

Map out a path you can take to treat each volunteer successfully under the conditions imposed by the chief medical officer.

Part B:

If the receptionist volunteers to be the 52nd recipient of the vaccine, and the same conditions apply, is Part A still possible? If not, prove it.

For your chance to win a $50 book voucher, send your solutions to by 5pm AEST Friday 30 July.

The answers will then be published on Actuaries Digital.


Volume 35 solutions

Congratulations to Daniel Smith, who correctly completed the Volume 35 Critical Line crossword puzzle! In doing so, Daniel earned himself a $50 book voucher.


Clue: a. Fabricated FBI fees intended predetermined payments (7,8)
Synonym: Predetermined payments
Cryptic solution: ‘Fabricated’ indicates an anagram of ‘FBI fees intended’.

Clue: b. Monitors what (l)-Across does? (9)
Synonym: Monitors
Cryptic solution: The solution to ‘(l)-Across’ is APRA, who regulate.

Clue: c. Sweatier substitution, so to speak (2,2,4)
Answer: AS IT WERE
Synonym: So to speak
Cryptic solution: ‘Substitution’ infers an anagram of ‘sweatier’.

Clue: d. Brown Gaussian leader has zest (4)
Answer: TANG Synonym: Zest
Cryptic solution: ‘Brown’ is TAN. ‘Leader’ indicates the first letter of ‘Gaussian’ ie G.

Clue: e. Random. Saint love lightspeed has endless tick (10)
Answer: STOCHASTIC Synonym: Random
Cryptic solution: ‘Saint’ is ST. ‘Love’ is O (tennis score). ‘Lightspeed’ is the constant C in physics. HAS is given. ‘Endless tick’ is clearly TIC.

Clue: f. Directionless Aus is a precious metal (4)
Answer: GOLD
Synonym: A precious metal
Cryptic solution: ‘Directionless’ indicates to take the compass point (S) off ‘Aus’ giving simply ‘Au’. On the periodic table Au is GOLD.

Clue: g. Bananas bare iron is like Covid transmission? (8)
Synonym: Like Covid transmission?
Cryptic solution: ‘Bananas’ indicates an anagram of ‘bare iron’.

Clue: h. A former President starts hackathon outdoor affairs with some builders (3,3)
Answer: HOA BUI
Synonym: A former President
Cryptic solution: ‘Starts’ indicates selecting the first letter of following words, ie HOA. ‘Some’ of
‘builders’ is BUI.

Clue: i. Hammered Herculean shin at Medicare (6,9)
Answer: HEALTH INSURANCE Synonym: Medicare
Cryptic solution: ‘Hammered’ means anagram ‘Herculean shin at’.

Clue: j. Bill butcher bet 500 (4)
Answer: DEBT Synonym: Bill
Cryptic solution: ‘500’ is D in Roman numerals. ‘Butcher’ infers to rearrange ‘Bet D’.

Clue: k. The most stylish I established after rating (9)
Synonym: The most stylish
Cryptic solution: ‘I established’ is IEST. This is placed ‘after’ another word for ‘rating’ ie CLASS.

Clue: l. Authority of scrap rations (abbrev.) (4) 
Answer: APRA
Synonym: Authority
Cryptic solution: ‘Of’ suggests the word is inside ‘scrAP RAtions’.

Clue: m. Imagine I eat inside delta and epsilon (6)
Answer: IDEATE
Synonym: Imagine
Cryptic solution: ‘I’ is given. ‘EAT’ is put inside ‘delta and epsilon’, i.e. DE. 

Clue: n. Molybdenum houses troubled torn lace simulation (5,5)
Synonym: Simulation
Cryptic solution: ‘Molybdenum’ is MO on the periodic table. ‘Troubled’ means anagram of ‘torn lace’ and this is ‘house(d)’ inside MO.


Clue: a. Premium heart at hothead such as algebra, calculus etc. (4) Answer: MATH
Synonym: Such as algebra, calculus etc.
Cryptic solution: The ‘heart” of ‘premium’ is M. ‘AT’ is given. ‘Hothead’, means ‘head’ of ‘hot’, i.e. H.

Clue: b. The Institute of odd piñatas (abbrev.) (3)
Answer: IAA
Synonym: The Institute
Cryptic solution: ‘Odd’ indicates every second letter of ‘piñatas’. 

Clue: c. Tin team leader greeting eye corners (6)
Answer: CANTHI
Synonym: Eye corners
Cryptic solution: A ‘tin’ is a CAN. ‘Team leader’ is T. A ‘greeting’ is HI.

Clue: d. Half the finances left the end (5)
Answer: FINAL
Synonym: The end
Cryptic solution: ‘Half’ of ‘finances’ is FINA. ‘Left’ is L.

Clue: e. We are after an endless module. Like | z | (7)
Synonym: Like | z |
Cryptic solution: ‘We’ is US. This is put ‘after’ ‘endless module’, ie MODUL.

Clue: f. Target date of French time. Such as x=y (8)
Synonym: Target date
Cryptic solution: ‘Of’ in ‘French’ is DE. ‘Time’ refers to the AD period. ‘x=y’ is a LINE.

Clue: g. North-East rising register to enroll (6)
Answer: ENLIST
Synonym: To enroll
Cryptic solution: ‘North-East rising’ infers writing ‘NE’ upwards since this is a down clue, giving EN. A ‘register’ is a LIST.

Clue: h. I left receipt with the French after current container (10)
Synonym: Container
Cryptic solution: ‘I left receipt’ means to take ‘I’ out, giving RECEPT. ‘The’ in French is LE and this is put ‘after’ a ‘current’ which is AC. 

Clue: i. Superannuation Guarantee in tatters. What a Fellow can do? (4)
Answer: SIGN
Synonym: What a Fellow can do?
Cryptic solution: ‘Superannuation Guarantee’ is SG. ‘IN’ is given. ‘Tatters’ means an anagram of these letters.

Clue: j. Loud wind is 50/50 (4)
Answer: FAIR
Synonym: 50/50
Cryptic solution: ‘Loud’ in music is F for fortissimo. ‘Wind’ is AIR.

Clue: k. Online education holds a necessity (4)
Answer: NEED
Synonym: A necessity
Cryptic solution: ‘Holds’ infers the answer is within ‘onliNE EDucation’.

Clue: l. At present, back after immense, large sets (3,4)
Answer: BIG DATA
Synonym: Large sets
Cryptic solution: ‘AT’ is given. The ‘present’ time is AD. These letters go ‘back’ forming DATA, and is
‘after’ ‘immense’, ie BIG.

Clue: m. The Author deals dreadfully (5)
Answer: SLADE
Synonym: The Author
Cryptic solution: ‘Dreadfully’ indicates to anagram ‘deals’.

Clue: n. Ominous oar is a return on asset (abbrev.) (3)
Answer: ROA
Synonym: A return on asset
Cryptic solution: ‘Ominous’ infers to rearrange ‘oar’.

Clue: o. About a 5 and 2.71828… To plunder (5)
Answer: REAVE
Synonym: To plunder
Cryptic solution: ‘About’ is RE (ie regarding). ‘A’ is given. ‘5’ in Roman numerals is V. 2.71828 is E.

Clue: p. Population studies massaged mode and chart with an unknown quantity (10)
Synonym: Population studies
Cryptic solution: ‘Massaged’ means rearrange ‘mode’ into DEMO. A ‘chart’ is a GRAPH. An
‘unknown quantity’ is Y.

Clue: q. Spurious sense sec cores (8)
Synonym: Cores
Cryptic solution: ‘Spurious’ indicates anagram of ‘sense sec’

Clue: r. Each Thursday in quarantine dining? (3,2)
Answer: EAT IN
Synonym: Quarantine dining?
Cryptic solution: ‘Each’ is EA. ‘Thursday’ is T. ‘In’ is IN.

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