It’s always rewarding to know that people read what you write. I was especially pleased to receive an email from a parent confirming they had read my column, until I realised they were reaching out to point out a mistake I had made! Yes, I did make an error in last week’s Parent Problem of the Week, the one about finding the lowest number that contains all the vowels and the letter ‘y’ when written out in words. I incorrectly stated that the answer was 6020, which does meet the criteria, but it’s not the lowest number. The correct answer is actually 1025. A big thank you to the parent who pointed this out (I’ll keep you anonymous)—I really do appreciate it.
Mistakes happen all the time, and learning from them is an essential part of developing a growth mindset, which is crucial for adapting to our ever-changing world. This also sparked my curiosity about significant instances where math errors caused major problems. Unfortunately, there have been many such incidents over time, and I’m going to share a few examples below. Please note that I’ve taken the stories from the following websites:
–https://mathspig.wordpress.com/category/lists/10-biggest-mathematical-disasters-in-the-world-lists/
–https://listverse.com/2019/08/30/10-simple-but-costly-math-errors-in-history/)
1. The unmanned NASA Mars Climate Orbiter reached Mars and executed a 16 minute 23 second main engine burn on 23rd September 1999 to establish an orbit around Mars at 150km. It orbited behind Mars and was never heard from again. As it turns out, the Mars Climate Orbiter, which cost £70 million, disappeared because a Lockheed Martin engineering team used Imperial measurements while the JPL (Jet Propulsion Lab) team used the more conventional metric system. The wrong navigation information was sent to the Mars Climate Orbiter. It most likely burnt up in the atmosphere.
2. In 2003, Spain launched the £2 billion S-80 submarine program to build four diesel-electric submarines for the Spanish navy. Spain had almost completed one of the submarines in 2013, when it discovered that the sub was 70 tons heavier than it should have been. The Spanish navy feared the submarine would never surface if it went underwater.
The submarine ended up heavy after someone put a decimal point in the wrong spot during calculations. No one discovered the error until the first submarine was completed, and the other three were already under construction. Ouch.
3. The Millennium Bridge (the suspension footbridge across the Thames River) cost £16 million and opened on 10th June 2000. It closed half an hour later as pedestrians were being knocked off their feet by the swaying bridge. The three big mistakes, often catastrophic, in engineering are maths, materials or human error. The Millennium Bridge was a maths problem. The bridge was designed in 2D. The engineers allowed for up and down movement but not sideways movement. The bridge’s movements were caused by a feedback phenomenon, known as ‘Synchronous Lateral Excitation’ or ‘wobbles’. It cost an estimated £5 million to resolve.
4. On July 1983, an Air Canada Boeing 767 flying from Ottawa to Edmonton with 69 passengers and crew had to crash-land after running out of fuel at 12,500 meters. The engines suddenly lost power, and the airplane started gliding to the ground. It glided for 100 kilometres before landing in Gimli, Manitoba. The accident was traced to a conversion error. Air Canada used the imperial system of measurement but was converting to the metric system, which this Boeing 767 already used. Air Canada ground crews had used the imperial system when they refuelled the airplane. They measured the fuel in pounds instead of kilograms. Because one kilogram equals 2.2 pounds it meant that the airplane had only around half the amount of fuel it required to complete the flight. The pilots did not notice the discrepancy because the fuel gauge was not working. Ground crews used drip sticks to measure the fuel at the time they filled the tanks.
Wishing everyone a lovely and restful half-term break.
Parent problem of the week
Complete the following with the digits 1 to 6 to make the sum correct. BIDMAS does NOT apply, so perform each mathematical operation in the order shown, from left to right, so 1 + 2 x 3 is treated as (1 + 2) x 3 = 9. Consecutive numbers are not next to each other, there is no ÷ 1, and at no point is a decimal or a fraction used.
……. + ……. – ……. x ……. / ……. x ……. = 50
Solution to last week’s problem
What is the least number of times you can use only the digit 2 to make a sum that gets to the total 23?
This question has many different solutions, and there is what I call a ‘cheat’ solution and then ‘non-cheat’ solutions.
The cheat solution requires the use of the digit ‘2’ four times. As you can see, you put two 2s together to make ‘22’, which is little bit of a cheat.
22 + (2/2) = 22 + 1 = 23
Then one non-cheat solution I worked out is to use the digit 2 eight times:
(22)2+22+2+(2/2)=16+4+2+1=23
However, the best non-cheat solution I could find online is a true masterpiece in the application of maths and requires the use of the digit 2 four times:
(2 + 2)! – 2 / 2 = 4! – 1 = 24 – 1 = 23
*Note that 4! (4 factorial) means 4x3x2x1 = 24.