The oldest pirate will propose a 98 : 0 : 1 : 0 : 1 split, in other words the oldest pirate gets 98 coins, the middle pirate gets 1 coin and the youngest gets 1 coin.

Let us name the pirates (from oldest to youngest): Alex, Billy, Colin, Duncan and Eddie.

Working backwards:

2 Pirates: Duncan splits the coins 100 : 0 (giving himself all the gold). His vote (50%) is enough to ensure the deal.

3 Pirates: Colin splits the coins 99 : 0 : 1. Eddie will accept this deal (getting just 1 coin), because he knows that if he rejects the deal there will be only two pirates left, and he gets nothing.

4 Pirates: Billy splits the coins 99 : 0 : 1 : 0. By the same reasoning as before, Duncan will support this deal. Billy would not waste a spare coin on Colin, because Colin knows that if he rejects the proposal, he will pocket 99 coins once Billy is thrown overboard. Billy would also not give a coin to Eddie, because Eddie knows that if he rejects the proposal, he will receive a coin from Colin in the next round anyway.

5 Pirates: Alex splits the coins 98 : 0 : 1 : 0 : 1. By offering a gold coin to Colin (who would otherwise get nothing) he is assured of a deal.

(Note: In the final deal Alex would not give a coin to Billy, who knows he can pocket 99 coins if he votes against Alex’s proposal and Alex goes overboard. Likewise, Alex would not give a coin to Duncan, because Duncan knows that if he votes against the proposal, Alex will be voted overboard and Billy will propose to offer Duncan the same single coin as Alex. All else equal, Duncan would rather see Alex go overboard and collect his one coin from Billy.)

S5/6 Maths

All pupils who picked Maths in S5/6 have been added to a Team. If you have not been added please let us know asap by emailing maths@coltnesshigh.n-lanark.sch.uk

S1-S3 Work

All work for S1-S3 is in your Team. Remember, if you have not been added to the Team please get in touch asap.

Daily Puzzle Fifty Four

5 pirates of different ages have a treasure of 100 gold coins.

On their ship, they decide to split the coins using this scheme:

The oldest pirate proposes how to share the coins, and ALL pirates (including the oldest) vote for or against it.

If 50% or more of the pirates vote for it, then the coins will be shared that way. Otherwise, the pirate proposing the scheme will be thrown overboard, and the process is repeated with the pirates that remain.

As pirates tend to be a bloodthirsty bunch, if a pirate would get the same number of coins if he voted for or against a proposal, he will vote against so that the pirate who proposed the plan will be thrown overboard.

Assuming that all 5 pirates are intelligent, rational, greedy, and do not wish to die, (and are rather good at math for pirates) what will happen?

Entry to National 4 Applications of Maths in S5/6

Attached is a pack of work for pupils who have picked Nat 5 Apps in S5/6. This work covers 24 periods worth of work and you should work through it over the months of May & June. Instructions on how to access the work and how to get in touch for help are included.

Entry to Nat 4 Apps

Add the contents of the first three pictures to get-

2 cats + 2 dogs + 2 rabbits = 10 + 20 + 24 = 54kg

So, 1 cat + 1 dog + 1 rabbit = 27kg

26

Let Holly’s number be x, then x2 – 20x = 156

Rearrange this to x2 – 20x – 156 = 0 and solve by factorising

(x + 6)(x – 26) = 0 so x = -6 or  x = 26, but since Holly is thinking of a positive integer, her number must be 26.

Entry to Higher Maths in S5/6

Attached is a pack of work for pupils who have picked Nat 5 Apps in S5/6. This work covers 24 periods worth of work and you should work through it over the months of May & June. Instructions on how to access the work and how to get in touch for help are included.

Entry to Higher Maths Pack

Functions and Graphs Notes

Graphicacy PowerPoint

Recurrence Relations Notes

Recurrence Relations PowerPoint

Straight Line PowerPoint

Straight Lines Notes

Trig Equations Nat 5 PowerPoint

Trig Graphs Nat 5 PowerPoint

Trigonometry Higher PowerPoint

Trigonometry Notes