The brainbuster
Find the solution to this brainbuster and win £200 of Amazon vouchers to spend on high-tech!
It's bonus time again at ACME Software!
In one small group, the six employees receive the following amounts: £3000, £3200, £3600, £3800, £4000, and one fortunate employee £6200.
The group comprises one engineer acting as manager, Team A with two employees and Team B with three.
One team receives a total bonus of exactly twice the amount as the other team.
Which bonuses are awarded to the manager, Team A and Team B? And can you demonstrate if/why your answer is the only possible solution?
Show your workings. Only complete entry forms will be considered. The judge's decision is final.
This competition closed on Sunday 25th August 2019.
The entries
There was a very good number of entries for this competition. As usual, nearly all entrants ended up with the correct answer, although some used rather more elegant approaches than others.
The solution
A solution as provided by our winner was:
Manager receives £4,000.
One member of Team A receives £3,000, the other receives £3,600, totalling £6,600 for Team A.
Members of Team B receive £3,200, £3,800 and £6,200, totalling £13,200 for Team B, which is twice Team A's total.
This is the only possibility as no other amount awarded to the manager leads to a remaining total which can be split into a ratio of 2:1 between the teams. Once it is decided that the manager receives £4,000, the distribution above is the only one which results in a 2:1 split with 3 people on Team B and 2 on Team A.
And the winner is...
Ben Dreux, a recent graduate in Mathematics from the University of Bath, is the winner of ECM's Brainbuster no. 45 competition...
...winning £200 of Amazon vouchers to spend on high-tech. Congratulations again to our winner, and watch out for ecm's next brainbuster!
