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This is the Transum Newsletter for the month of April 2024. It begins, as usual with the puzzle of the month.
A - 3B + 5C = 37
3A + 7B - C = 47
A + B + C = D
What is the value of D?
Please let me know if you solve the puzzle. I'd love to hear how you solved it (or your students solved it). Drop me an email at: gro.musnarT@rettelsweN
While you think about that here are some of the key resources added to the Transum website during the last month.
Pythagorean Probe is a multi-level set of self-marking exercises that begins with straight forward applications of Pythagoras' Theorem and leads or 'probes' a lot deeper with algebraic puzzles. All answers are integers so a knowledge of the Pythagorean triples would be an advantage.
Captain Obvious always gives the most predictable answers to Maths questions. Think outside the box by playing The Uniqueness Game:
This new whole-class game was inspired by an excellent resource shared on social media by @JohnRubinstein1. Six categories are displayed on the whiteboard for all the students to see. Their task is to think of an example for each of the categories but to make their choices unusual. Captain Obvious has already determined the predictable, vanilla, common example and students will earn more points if their choices are not the same as his. Mini-whiteboards would be perfect for this activity. I no longer have a class with which to try this activity so please let me have feedback if you play this game with your class.
This newsletter was published on 1st April which many will know as April fool’s day; the day when people play practical jokes and hoaxes on each other.The Starter of the day for the 1st is called One out of Ten and is a cunning way you can enjoy the fun of this special day at the expense of your students. Be sure to do it before midday though because that’s when you licence to fool expires (or so I remember from childhood days).
Exam season is just around the corner and there are so many ways the Transum website can be used to help students revise. Firstly there’s the Exam-Style questions which are all slightly different versions of questions that have appeared on exam papers in recent years. The Foundation level questions are presented as self-marking exercises while the more advanced level questions are presented with worked solutions. In addition there’s a Revision page with helpful advice and resources. Feel free to share the links with your students.
Don't forget you can listen to this month's podcast which is the audio version of this newsletter. You can find it on Spotify or Apple Podcasts. You can follow Transum on Twitter and 'like' Transum on Facebook.
Finally the answer to last month's puzzle which was: Given Easter egg baskets that come in packs of 5, 12, and 18, what is the largest number of eggs that cannot be purchased using a combination of these pack sizes?
The answer is 31.
The first five people to send in correct answers were Kevin, Chris, Rick, Søren and George. Some of their answers can be seen below.
This puzzle was based on a classic example of the Chicken McNugget Theorem (also known as the Frobenius Coin Problem or the Frobenius Problem) which Howie demonstrates in a short video. There are more Easter activities here.
That's all for now,
John
PS. There are 10 types of people in this world. Those who understand binary and those who don't.
Do you have any comments? It is always useful to receive feedback on this newsletter and the resources on this website so that they can be made even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.
Kevin Wallis,
Friday, March 1, 2024
"Good morning/evening
I think the answer is 31.
5 helps with everything
Number ending in 0 (5+5)
Number ending in 1 (3x12+5) 41 highest
Number ending in 2 (12)
Number ending in 3 (18+5)
Number ending in 4 (12+12)
Number ending in 5 (5)
Number ending in 6 (3 x 12 or 2 x 18)
Number ending in 7 (5+12)
Number ending in 8 (18)
Number ending in 9 (2 x 12 + 5)
Then the next number ending in 0 can be generated by adding 5+5 and similar for all numbers. "
Chris Smith,
Friday, March 1, 2024
"The answer to your puzzle is the Frobenius Number for 5,12,18. Wolfram Alpha has a widget for that:
"Find Your Frobenius"
It tells me that 31 is the largest number that can’t be made and I can prove that there are none higher:
32 is ‘12,5,5,5,5’
33 is ‘18,5,5,5’
34 is ‘12,12,5,5’
35 is ‘5,5,5,5,5,5,5’
36 is ‘18,18’
Now that we have five in a row that are possible I can simply keep adding 5 to each of these numbers forever to obtain every number from 32 onwards!"
Rick,
Saturday, March 2, 2024
"The number cannot end in 0 or 5, since that could be paid for with a multiple of 5 egg baskets.
Any number greater than 31 ending in 1 can be paid for with a multiple of 5 and 18 egg baskets.
Any number greater than 2 ending in 2 can be paid with a multiple of 12 and 5 egg baskets.
Any number greater than 13 ending in 3 can be paid for with a multiple of 5 and 18 egg baskets.
Any number greater than 14 ending in 4 can be paid for with a multiple of 5 and 12 egg baskets.
Any number greater than 16 ending in 6 can be paid with a multiple of 5 and 12 egg baskets.
Any number greater than 7 ending in 7 can be paid for with a multiple of 5 and 12 egg baskets.
Any number greater than 8 ending in 8 can be paid for with a multiple of 5 and 18 egg baskets. Any number greater than 19 ending in 9 can be paid for with a multiple of 5 and 12 egg baskets.
This leaves 31 as the highest number that cannot be paid for with the baskets."
Søren,
Wednesday, March 6, 2024
"Hi there
My students - 4th grade - tried combinations for different numbers and concluded that 31 is the largest number that you can’t make from the three basket sizes.
Are they correct? "