# Brainteasers

15th April 2005 at 01:00
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.

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