Uploaded January 2023 | Updated September 2026, 2 weeks ago
Can you measure 1ml of water using unmarked beakers of size 5ml and 7ml? Learn how to solve tech interview "measuring questions" using Bezout's Lemma.
We begin by filling and emptying the beakers until we arrive at a solution. By analysing what we have done, we are able to convert the problem into an algebraic equation known as a Linear Diophantine Equation. The solvability of Linear Diophantine Equations is then discussed by introducing the concept of "greatest common divisor" (GCD) and the definition of "co-prime".
A further application of Bezout's Lemma to the Chinese Zodiac Calendar is explored by introducing the concepts of "leat common multiple" (LCM) and the 'Chinese Remainder Theorem".
Produced by TRM intern Shucheng Li with assistance from Dr Tom Crawford. Shucheng is a second year mathematics undergraduate at the University of Oxford. Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: seh.ox.ac.uk/people/tom-crawford
If you would like to take part in the Tom Rocks Maths intern scheme, please get in touch using the contact form on the TRM website: tomrocksmaths.com/contact
For more maths content check out Tom's website tomrocksmaths.com
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
facebook.com/tomrocksmaths
twitter.com/tomrocksmaths
instagram.com/tomrocksmaths
Get your Tom Rocks Maths merchandise here:
beautifulequations.net/collections/tom-rocks-maths
Can you measure 1ml of water using unmarked beakers of size 5ml and 7ml? Learn how to solve tech interview "measuring questions" using Bezout's Lemma.
We begin by filling and emptying the beakers until we arrive at a solution. By analysing what we have done, we are able to convert the problem into an algebraic equation known as a Linear Diophantine Equation. The solvability of Linear Diophantine Equations is then discussed by introducing the concept of "greatest common divisor" (GCD) and the definition of "co-prime".
A further application of Bezout's Lemma to the Chinese Zodiac Calendar is explored by introducing the concepts of "leat common multiple" (LCM) and the 'Chinese Remainder Theorem".
Produced by TRM intern Shucheng Li with assistance from Dr Tom Crawford. Shucheng is a second year mathematics undergraduate at the University of Oxford. Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: seh.ox.ac.uk/people/tom-crawford
If you would like to take part in the Tom Rocks Maths intern scheme, please get in touch using the contact form on the TRM website: tomrocksmaths.com/contact
For more maths content check out Tom's website tomrocksmaths.com
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
facebook.com/tomrocksmaths
twitter.com/tomrocksmaths
instagram.com/tomrocksmaths
Get your Tom Rocks Maths merchandise here:
beautifulequations.net/collections/tom-rocks-maths
