# Brainteasers

Bean bags

Nasser throws some bean bags.

Each on lands in a bucket.

More than one bag can land in a bucket.

* What is the highest score that Nasser can get with 3 bean bags?

* Find three different ways that Nasser can score 15 with 3 bean bags.

* How many different scores can Nasser get with just 2 bean bags?

Football league

In a football league with 5 teams, each team plays 5 games with each of the other 4 teams, a total of 20 games per team.

Each game ends in a win, loss or draw.

The table shows the number of games won, lost or drawn for each team at the end of the season.

Nod-7 How many games did the Eagles win, lose and draw in the season?

SOLUTIONS Bean bags (ages 5 to 7) Highest score with 3 bags is 21. Nasser can score 15 with 5, 5, 5 or 7, 7, 1 or 7, 5, 3. Possible scores from 2 bags are 2, 4, 6, 8, 10, 12, 14.

Football league (ages 10 to 14) Eagles won 19 games, lost no games and drew 1 game. Eagles play 20 games so a + b + c = 20 where a, b and c are integers such that 0 2 a 2 20, 0 2 b 2 20, 0 2 c 2 20. The total number of games won by all the teams must equal the total number of games lost, so 25 + a = 44 + b. Substituting gives 2b + c = 1. The only possible solutions are b = 0, c = 1, and a = 19.

It only takes a moment and you'll get access to more news, plus courses, jobs and teaching resources tailored to you

## Latest stories

• ### Three new judges for Tes FE Awards

Julia Belgutay
14 August 2018
• ### Crowdfunding raises £20,000 to get girls into Stem

Kate Parker
14 August 2018
• ### A-level results day: 'We must change university admissions'

John Dunford
14 August 2018
• ### Banned: Ex-con teacher who hid crimes from school

Martin George
14 August 2018
• ### A-level results: three questions for students who miss offers

Elliot Douglas
14 August 2018
• ### Is there a battle brewing over Ofsted’s curriculum plans?

Ed Dorrell
14 August 2018
• ### DfE court loss gives SEND pupils exclusion protection

Helen Ward
14 August 2018
• ### A-level results day 2018: Help with clearing

Mark Heaton
14 August 2018
• ### 'FE needs to be the leader, not the the supportive team-player'

Mark Dawe
14 August 2018
• ### 'A levels are about more than just results'

Paul Whiteman
14 August 2018