Four Cadets, Four Duties, Four Service Lengths
A four-person detachment at a forward airfield must fill four duties every day - signaller, driver, medic and marksman - with exactly one soldier per duty. The four soldiers are Kiptoo, Wanjiku, Otieno and Mwangi, and each has a different length of service: one, two, three or four years. The duty officer's notebook has lost a page and only the following entries survive:
- Wanjiku has served two years.
- The driver has served longer than Wanjiku but less than Otieno.
- Mwangi is the marksman.
- Wanjiku is not the medic.
The radio set is old, and the standing order is that only a soldier with two or more years of service may operate it as signaller. Nobody may hold two duties on the same day and every duty must be filled. The commander needs the duty list before the 0600 briefing, and has said she will not accept 'probably' - she wants one answer and the reasoning that forces it.
1. Produce the complete duty list with each soldier's years of service, showing why each step is forced rather than guessed.
Read the worked answer
Work from the clue that constrains most, and let each result eliminate options.
Step 1 - pin the driver and Otieno. Clue 2 says the driver's service is strictly between Wanjiku's (2 years, clue 1) and Otieno's. The only available whole numbers are 1–4, and the driver must be greater than 2 but less than Otieno. The only possibility is driver = 3 years and Otieno = 4 years. Nothing else fits.
Step 2 - identify the driver. The driver has 3 years. Wanjiku has 2 and Otieno has 4, so neither can be the driver. Mwangi is the marksman (clue 3) and cannot hold two duties, so Mwangi is not the driver either. Therefore Kiptoo is the driver with 3 years.
Step 3 - remaining years. Wanjiku 2, Kiptoo 3, Otieno 4, so Mwangi has 1 year.
Step 4 - remaining duties. Kiptoo is the driver and Mwangi the marksman, leaving signaller and medic for Wanjiku and Otieno. Clue 4 removes Wanjiku from the medic, so Wanjiku is the signaller and Otieno is the medic.
Step 5 - check against the standing order. The signaller must have two or more years. Wanjiku has exactly two, so the list is legal.
Answer: Kiptoo - driver, 3 years; Wanjiku - signaller, 2 years; Otieno - medic, 4 years; Mwangi - marksman, 1 year.
Notice that the standing order did no work in the deduction. It only confirmed the answer. Mixing up a confirmation with a constraint is the commonest error in this kind of question.
2. Which single clue is doing the most work, and what happens to the answer if that clue is lost? Show the alternatives rather than just naming the clue.
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The load-bearing clue is clue 4 - 'Wanjiku is not the medic'.
Remove it and re-run the deduction. Steps 1 to 3 are unaffected: Kiptoo is still the driver with 3 years, Mwangi the marksman with 1 year, Otieno on 4, Wanjiku on 2. The signaller and medic duties are still shared between Wanjiku and Otieno, but nothing now decides which.
Two candidate lists survive:
- (a) Wanjiku - signaller, 2 years; Otieno - medic, 4 years.
- (b) Wanjiku - medic, 2 years; Otieno - signaller, 4 years.
Does the standing order break the tie? No. It requires two or more years for the signaller, and both 2 and 4 satisfy it. A constraint that both alternatives pass is not a tie-breaker.
What this teaches. With clue 4 missing, the honest answer to the commander is 'two legal lists, here they are, choose one and I will record why'. Presenting list (a) alone as if it were derived would be a guess dressed as a deduction. If a tie-breaker were genuinely needed, it must be a stated rule - for example, the senior soldier takes the radio - and it should be written into the standing orders afterwards so that the next duty officer does not face the same ambiguity.
Also note: clue 1 is needed twice, once to fix the ordering range and once to establish the signaller's eligibility, so it cannot be discarded either. Clue 3 is needed to keep Mwangi out of the driver's seat. Only clue 4 is redundant to the years and essential to the duties.
3. A fifth soldier, Chebet, arrives with five years of service and is immediately assigned the driver duty. What can now be determined, and what cannot?
Read the worked answer
What is fixed. Chebet is the driver (given) and Mwangi remains the marksman. Kiptoo is released from the driver duty and joins Wanjiku and Otieno in the pool for the two remaining duties, signaller and medic. The years are unchanged for the original four, and Chebet's five years are simply outside the 1–4 range and irrelevant to any other clue.
What is not fixed. There are now five soldiers for four duties, so one soldier stands down each day, and three people (Kiptoo, Wanjiku, Otieno) compete for two posts. Clue 4 still bars Wanjiku from the medic. Enumerate:
- Wanjiku is signaller. The medic is either Kiptoo or Otieno; the other stands down. → 2 arrangements.
- Wanjiku stands down. Signaller and medic are split between Kiptoo and Otieno in either order, and both have two or more years, so the standing order permits both. → 2 arrangements.
- Wanjiku is medic - barred by clue 4.
Four legal arrangements. The commander cannot be given one list without a further stated rule.
Judgement point. The temptation is to assume the new arrival changes nothing because she is 'outside' the original puzzle. She changes everything, because she displaces the soldier who was pinned by the ordering clue. The correct response is not to invent an answer but to say plainly: 'Four valid duty lists; I need one more rule, or your decision on which of these four you prefer.' A cadet who states four possibilities with reasons is more useful than one who states one possibility with false confidence.