The journey of every round

Applicant is 28 weeks pregnant with no other children, single, fleeing domestic abuse from her partner; she presented to a London borough on 11 April 2025. Council accepts she is homeless and eligible but is taking the position that priority need under section 189(1)(a) Housing Act 1996 only attaches "from the date of birth or 29 weeks gestation". Applicant relies on the gestational-stage caselaw. Is the council's interpretation of priority need defensible?

Applicant is sofa-surfing at a friend's two-bed flat in Birmingham; the friend has told her in writing on 2 April 2025 she must leave by 30 April 2025. Applicant approached the council on 7 April 2025. The duty officer told her she is "not homeless or threatened with homelessness" because she "has accommodation tonight". Under section 175(4) Housing Act 1996 (as amended by the Homelessness Reduction Act 2017) and the Code of Guidance, when does the prevention duty under section 195 trigger?

Applicant left a privately rented two-bed flat on 14 January 2025 after two months of escalating anti-social behaviour from the upstairs neighbour, including threats to her child witnessed by police on 8 January 2025 (no charges brought). She approached Manchester City Council on 20 January 2025; the council issued a section 184 decision on 28 March 2025 finding her intentionally homeless because "she had a tenancy she could have remained in". Is the council's intentionality finding likely to survive section 191(1) Housing Act 1996 challenge on review?

Tenant did not give written notice of a slow shower drain at a first-floor flat that ran from June 2024; on 3 February 2025 a blocked drain caused a flood damaging the tenant's furniture. Tenant claims under section 11 LTA 1985 for the damaged items. Landlord argues no liability because notice of the disrepair was never given. Does the implied repairing covenant require notice of the disrepair, and does the answer differ for common parts the landlord retains control of?

Mould is visible on the bedroom wall behind the wardrobe at a flat let from 1 November 2023; landlord's surveyor reports it as "condensation caused by tenant lifestyle — windows kept shut, drying laundry indoors". Tenant points to a defective extractor fan in the bathroom and single-glazed windows in the bedroom. Tenant intends to bring a claim under section 9A of the Landlord and Tenant Act 1985 (Homes (Fitness for Human Habitation) Act 2018). Whose evidential burden is it to show the cause and what does the case law say about lifestyle-vs-defect causation?

Tenant reported a leaking bathroom waste pipe by WhatsApp on 4 January 2025 and again by email on 18 January 2025; landlord's letting agent acknowledged the email but no repair occurred until 22 April 2025 when ceiling staining appeared in the kitchen below. Tenant is considering a disrepair claim. Does this timeline establish breach of section 11 of the Landlord and Tenant Act 1985 and from what date does the breach run?

A landlord let a property from 1 May 2022 to 30 April 2024 across two consecutive 12-month fixed-term tenancies with the same tenant. The £1,800 deposit was protected for the first tenancy in May 2022 with TDS but no fresh prescribed information was served when the second fixed-term AST was signed on 1 May 2023. Tenant left and is now claiming compensation under section 214 Housing Act 2004. Does the deemed-renewal rule (Superstrike line) apply or does the fresh fixed term break it?

Deposit of £1,200 was protected within 14 days in the DPS custodial scheme. The prescribed information given to the tenant lists the landlord as "J. Patel" but the landlord's full name on the AST is "Jaspreet Singh Patel" and the address for service shown is the letting agent's office rather than the landlord's own address. Tenant has been served Section 21. Is the prescribed information defective for the purposes of section 213(6) Housing Act 2004?

Tenant paid £1,650 deposit on 12 March 2024 for a tenancy commencing 1 April 2024 at 22 Cedar Lane, Sheffield. Landlord protected the deposit with mydeposits on 28 May 2024 (57 days after receipt) and served the prescribed information the same day. Landlord now wants to serve Section 21 in May 2025. What is the legal position under sections 213-215 of the Housing Act 2004 as amended by the Deregulation Act 2015?

A five-bedroom house in Nottingham has a mandatory HMO licence issued June 2023 for five occupiers. The licensee converted the dining room to a sixth bedroom in November 2024 and let it to a sixth sharer without notifying the council. The council inspected on 2 April 2025 and is now considering a financial penalty under section 249A HA 2004. Is the licensee's position that "the licence covers the house, not headcount" defensible?

Owner-occupier lives in the ground-floor flat of a converted Victorian house in Bristol and lets the upper two floors on a single AST to a couple plus their adult son and one lodger of the son — four occupiers over two floors above the owner. The owner argues this is a "resident landlord" arrangement excluded from HMO definition. Does HA 2004 section 254(2) HMO definition still capture the upper-floor letting?

A three-storey terraced house at 47 Beechwood Road, Leeds is let on five separate ASTs to five unrelated professionals sharing kitchen and bathroom; landlord has not applied for any licence. Leeds City Council has additional licensing only in the LS6 ward (this property is LS8). Does the property require a mandatory HMO licence under section 55 of the Housing Act 2004?

Landlord served Form 6A Section 21 on 3 February 2025 for a tenancy that began 5 October 2023. The gas safety certificate covering the period from 5 October 2023 was carried out on 2 October 2023 but was only handed to the tenant on 12 February 2025 alongside the s21 notice. Is the s21 valid given the Trecarrell-line authorities on late provision of the gas certificate?

Tenancy began 12 June 2023 on a 12-month fixed term; rolled periodic in June 2024; landlord served a Form 6A Section 21 on 8 April 2025 expiring 9 June 2025. The How to Rent guide given at sign-up was the January 2020 edition (current edition at service of notice was March 2023). Does the outdated How to Rent guide invalidate the Section 21?

On 14 March 2025 my landlord handed me a one-page note saying "vacate by 14 May 2025"; the AST started 1 September 2023 and rolled to a statutory periodic in September 2024, rent paid monthly on the 5th. The note is not on Form 6A. Can a court accept this as a valid Section 21 notice if the landlord later issues accelerated possession proceedings?

Given f(x) = (x - 4) / 3, state the inverse function f^(-1)(x). Give the inverse in explicit form.

State the distributive law of intersection over union for three sets A, B, C. Give the identity in set notation.

State the formula for the volume of a sphere of radius r. Give the formula in exact form using pi.

Given the recursive sequence a_1 = 2 and a_(n+1) = 3 a_n - 1, compute a_4. Give the exact integer.

Compute the limit of the sequence a_n = (5n^2 + 2) / (2n^2 - n + 4) as n approaches infinity. Give the exact value.

Compute the sum of the arithmetic series 3 + 7 + 11 + ... + 99. Give the exact integer.

Compute the sum of the infinite geometric series 1 + 1/3 + 1/9 + 1/27 + ... Give the exact value.

Is the repeating decimal 0.999... equal to 1? State the exact value and justify using a geometric-series argument.

How many distinct arrangements are there of the letters in the word "STATISTICS"? Give the exact integer.