QE boys have performed strongly in an online national Mathematics competition, with two teams winning prizes – one for being the first team in the country to solve two of the puzzles.
The high-speed solutions to puzzles 3 and 5 in the MathsBombe competition came from Sixth-Form team Root to Success. The team, comprising Year 13 pupils Brian Kong, Zayaan Ahmad, Yuta Tsuchiya and Nitharsan Sathiyalingam, all plan to read Mathematics at university. Zayaan said he had particularly enjoyed the “intricate” nature of the puzzles.
Year 12 team Pablo Problems won a spot prize for puzzle 8. (The spot prizes were awarded at random and were open to all teams that had solved a problem correctly.) The team members were Abhishek Balkrishna, Shiran Gnanaraj, Oliver Robinson and Vigneswaran Thelaxshan.
MathsBombe, which is run by Manchester University, started on 18th January this year; a new pair of puzzles was then released every two weeks. The MathsBombe website states that these puzzles “span the whole spectrum of mathematics: from fiendish logic puzzles in pure mathematics to applications of mathematics in real-world settings”.
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Teams were ranked firstly in order of the number of puzzles they had solved and then by the total number of points scored for each correctly solved puzzle. Points were based on the teams’ speed of response, with the maximum number of 15 awarded to teams submitting the correct solution within one hour of the first team to solve the puzzle.
Just 47 teams out of the 2,962 teams entering nationally solved all eight puzzles. The 47 included five from QE: Pablo Problems, We Da Bomb, Test Maths Team V2, Pie R squared and 1 Elite Maths. Although Root to Success appeared to be on track for a high position after the four boys achieved the maximum 15 points in all of the first six puzzles, they then slipped down the rankings because they were unable to solve the final two puzzles. The final overall results have yet to be announced.
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Congratulating the successful teams, QE’s Assistant Head of Mathematics Wendy Fung said: “All the boys have worked entirely independently. The competition was a great chance for the members of Root to Success to test their problem-solving skills ahead of university.”
The competition is supported by the Dame Kathleen Ollerenshaw Trust, named after a mathematician and astronomer who also served as Lord Mayor of Manchester.
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This is puzzle 3, which Root to Success solved in double-quick time:
A miserly billionaire stores UK coins in a giant silo to avoid paying tax. Coins are released by turning a giant crank attached to the silo, but only one coin is released for each turn of the crank. The billionaire requires 60 coins of identical value. Assuming that the silo contains an infinite supply of coins of every possible denomination in standard circulation (ignoring any special commemorative coins), how many turns of the crank are needed to guarantee this?
And here is the solution provided by the competition organisers:
At first sight, it appears that there is not enough information to answer this problem, but the point is that it doesn't matter what the value of the 60 coins is. Thus, the worst case is actually that we get a different coin for each turn of the handle until we get up to 59 coins for every denomination. The next turn of the crank must then guarantee 60 coins of identical value. There are eight possible denominations: 1p, 2p, 5p, 10p, 20p, 50p, £1 and £2, which means that the number of turns required is 8 x 59 + 1 = 473.