Six themes emerge from the ideas that have been chosen as finalists in the Mayors Challenge competition run by Bloomberg Philanthropies that give an insight into the preoccupations of European public administrations.

That cities should learn from each other's successes and failures is a basic principle of urbanism and one that is at the heart of the Mayors Challenge, which this year is focused on Europe.

The finalist cities have been chosen on the quality of innovative ideas that their town halls propose to implement, which hope to solve social, economic and environmental problems, and provide examples of best practice that can be shared with other cities.

There are six emergent themes evident among these ideas that are emblematic of problems faced by cities everywhere: civic engagement, unemployment, health, climate change, transport and crime, with the quality of housing being a sub-theme.

Chosen from 155 applicants among cities in the 40 countries of Europe with populations over 100,000 and densities greater than 20 residents per hectare, the 21 finalists will now go on to meet, exchange and refine their ideas, attending an Ideas Camp in June, before the winners are selected in the Fall.

One city will win a prize of €5 million to put their plan into action, and four other cities will win €1 million each. Participants will join an international network of creative cities to tackle problems together and learn from their best practices.

James Anderson, the head of government innovation for Bloomberg Philanthropies, said: "The ideas tended toward networked, distributed solutions as opposed to costly centralized ones. There was a lot of interest in citizen engagement as both a means and end. Technology that concretely and positively affects the lives of individual citizens – from the blind person in Warsaw to the unemployed youth in Amsterdam to the homeowner in Schaerbeek - also played a significant role."

Of the 21 finalist cities, five are from the United Kingdom: Bristol, Cardiff, Kirklees, London and York.

Civic engagement

Surprisingly, perhaps, for a city emerging from years of chaos, Athens is on the list. Its proposal is to create an online platform to connect civic society, an idea that is also shared by Gdansk in Poland.

This popular theme is also taken up by The Hague, Netherlands, which is hoping to encourage public participation in decision-making, adding gaming and crowd-sourcing to the tools on offer.

York, UK, also shares this theme, confining the trawl for peoples' suggestions to ways of revolutionising public procurement, while Sofia in Bulgaria will use mobile art workshops to solicit residents' views on the redesign of public spaces.

Unemployment

Unemployment is another theme, being tackled by several cities. Amsterdam wants to use an online gaming platform to train at young people to be attractive to employers).

Stara Zagora, in Bulgaria, hopes to encourage back some of the 97% of young people who leave to study elsewhere and never return, by offering start-up funding and incentives for those willing to take up science-based ventures.

The beautiful, historic city of Florence, in Italy, has two out of every five commercial properties vacant and will utilise this space by giving it to artisans as a means of revitalising neighbourhoods.

Still in Italy, Bologna, will also tackle youth unemployment by partnering with local entrepreneurs to teach computer coding and other modern skills to young people; and Bristol, UK, who solution also addresses the problem of obesity with a proposal to create jobs by providing locally grown healthy food.

Health

Health, in fact, is also a popular theme, addressed by three other cities: Barcelona, with a high proportion of residents over 65, proposes strategies to encourage communities to look after the elderly; Cardiff, Wales, will be encouraging people to partake in sporting activities.

 London proposes to introduce apps and sensors to help citizens monitor their own health and governments to spot at-risk patients.

Finally, Warsaw in Poland wants to deploy high-tech auditory alerts around the city to enable blind and visually impaired people to navigate around as easily as the sighted.

Climate change

Tackling climate change, unsurprisingly, also figures high. Stockholm proposes to encourage citizens to produce biochar from their green waste and is it in their gardens to sequester carbon; while Lisbon hopes to tap into a previously unused source of energy: kinetic energy generated by commuting traffic, turning it into electricity.

Madrid aims to set up a social enterprise to harvest geothermal energy and waste heat; while Schaerbeek, Belgium, proposes to use 3-D geothermal mapping technology to create personalised energy guides for each residence and use them to provide plans for citizens to help them save energy in their homes.

Transport

The theme of transport is only tackled by one city: Kraków in Poland hopes to develop an incentive programme that will reward people with tax breaks and discounts for choosing green transit modes.

Crime

Crime is the final emergent theme. Located in the Czech Republic, Brno, like many cities in Eastern Europe, is blighted by large, crime-ridden, deprived, housing estates. Its idea tackle the problem is to train and engage citizens to become a new generation of 'concierges'.

"European cities in this year's Mayors Challenge stepped up with bold and creative ideas that have the potential to improve lives across the continent and globe,"  commented Michael R. Bloomberg, the former Mayor of New York City who is behind the competition. "Cities face many urgent challenges. We need city leaders to continually reach for innovative new ways to address urban challenges – and then share what's working with the world. That's what the Mayors Challenge is all about."

The 2013-2014 Mayors Challenge is Bloomberg Philanthropies' first in Europe after the inaugural competition in the United States.