0

1

2

3

4

5

6

7

8

9

Using the digits 0 to 9 to form five 2 digit numbers which are all multiples of three.

#### Hot Numbers Interactive

If you have access to computers, iPads or slates, this is the interactive version of this activity.
www.transum.org/go/?to=hot

#### Hot Number Challenges

www.transum.org/go/?to=hotchallenges

Share

Topics: Starter | Number

• 9 Yellow, St Peters High School
•
• "very good for a warm up activity" "kept mind active" from students.
The whole class could access this and 6 students were totally engrossed for virtually the whole lesson, wanting to move to the higher levels
• Y5, St Nicholas
•
• We found another solution: 12, 36, 90, 87, 54.
We enjoyed it! It was fun!
• Mr Shepherd, St Lawrence Academy, Scunthorpe
•
• Interesting extension for smart groups: How many different answers are there? This can be worked systematically by groups who know the "digit sum" rule for multiples of 3.
WORKING IT OUT (try it yourself first if you like):
The 1, 4 and 7 can only go with a 2 or 5 or 8
There are 6 possible pairings of these numbers.
Each of these two digit numbers can be reversed, so there are 2 cubed combinations once the 2-digit numbers are chosen.
The remaining digits 0,3,6,9 can be paired 3 ways.
In each case, a pairing contains a zero, and we assums that the zero cannot go first in a 2-digit number, so there are only two possibilities once pairings are chosen.
Overall then, the number of combinations (answers), ignoring their position on the answer grid (which would multiply the answer by 5 factorial), is:
6 x 2cubed x 3 x 2 = 288.
• Matthew, 3D, Craigslea State School
•
• I found these:
15, 24, 30, 69 and 78.
• Transum,
•
• Thanks to everyone for their comments. Yes this certainly is a worthwhile activity providing access to pupils of all abilities. It also lends itself to extension questions such as that suggested by Mr Shepherd (all 288 possible solutions are provided in the answer section below). If your pupils have access to computers, ipads etc it's a good idea to use the self-checking, multi-level version of this activity available here: Hot Numbers Interactive. Enjoy.

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.

If you don't have the time to provide feedback we'd really appreciate it if you could give this page a score! We are constantly improving and adding to these starters so it would be really helpful to know which ones are most useful. Simply click on a button below:

Excellent, I would like to see more like this
Good, achieved the results I required
Satisfactory
Didn't really capture the interest of the students
Not for me! I wouldn't use this type of activity.

This starter has scored a mean of 3.1 out of 5 based on 440 votes.

Previous Day | This starter is for 2 December | Next Day

 12, 30, 45, 69, 7812, 30, 45, 69, 8712, 30, 45, 78, 9612, 30, 45, 87, 9612, 30, 48, 57, 6912, 30, 48, 57, 9612, 30, 48, 69, 7512, 30, 48, 75, 9612, 30, 54, 69, 7812, 30, 54, 69, 8712, 30, 54, 78, 9612, 30, 54, 87, 9612, 30, 57, 69, 8412, 30, 57, 84, 9612, 30, 69, 75, 8412, 30, 75, 84, 9612, 36, 45, 78, 9012, 36, 45, 87, 9012, 36, 48, 57, 9012, 36, 48, 75, 9012, 36, 54, 78, 9012, 36, 54, 87, 9012, 36, 57, 84, 9012, 36, 75, 84, 9012, 39, 45, 60, 7812, 39, 45, 60, 8712, 39, 48, 57, 6012, 39, 48, 60, 7512, 39, 54, 60, 7812, 39, 54, 60, 8712, 39, 57, 60, 8412, 39, 60, 75, 8412, 45, 60, 78, 9312, 45, 60, 87, 9312, 45, 63, 78, 9012, 45, 63, 87, 9012, 48, 57, 60, 9312, 48, 57, 63, 9012, 48, 60, 75, 9312, 48, 63, 75, 9012, 54, 60, 78, 9312, 54, 60, 87, 9312, 54, 63, 78, 9012, 54, 63, 87, 9012, 57, 60, 84, 9312, 57, 63, 84, 9012, 60, 75, 84, 9312, 63, 75, 84, 9015, 24, 30, 69, 7815, 24, 30, 69, 8715, 24, 30, 78, 9615, 24, 30, 87, 9615, 24, 36, 78, 9015, 24, 36, 87, 9015, 24, 39, 60, 7815, 24, 39, 60, 8715, 24, 60, 78, 9315, 24, 60, 87, 9315, 24, 63, 78, 9015, 24, 63, 87, 9015, 27, 30, 48, 6915, 27, 30, 48, 9615, 27, 30, 69, 8415, 27, 30, 84, 9615, 27, 36, 48, 9015, 27, 36, 84, 9015, 27, 39, 48, 6015, 27, 39, 60, 8415, 27, 48, 60, 9315, 27, 48, 63, 9015, 27, 60, 84, 9315, 27, 63, 84, 90 15, 30, 42, 69, 7815, 30, 42, 69, 8715, 30, 42, 78, 9615, 30, 42, 87, 9615, 30, 48, 69, 7215, 30, 48, 72, 9615, 30, 69, 72, 8415, 30, 72, 84, 9615, 36, 42, 78, 9015, 36, 42, 87, 9015, 36, 48, 72, 9015, 36, 72, 84, 9015, 39, 42, 60, 7815, 39, 42, 60, 8715, 39, 48, 60, 7215, 39, 60, 72, 8415, 42, 60, 78, 9315, 42, 60, 87, 9315, 42, 63, 78, 9015, 42, 63, 87, 9015, 48, 60, 72, 9315, 48, 63, 72, 9015, 60, 72, 84, 9315, 63, 72, 84, 9018, 24, 30, 57, 6918, 24, 30, 57, 9618, 24, 30, 69, 7518, 24, 30, 75, 9618, 24, 36, 57, 9018, 24, 36, 75, 9018, 24, 39, 57, 6018, 24, 39, 60, 7518, 24, 57, 60, 9318, 24, 57, 63, 9018, 24, 60, 75, 9318, 24, 63, 75, 9018, 27, 30, 45, 6918, 27, 30, 45, 9618, 27, 30, 54, 6918, 27, 30, 54, 9618, 27, 36, 45, 9018, 27, 36, 54, 9018, 27, 39, 45, 6018, 27, 39, 54, 6018, 27, 45, 60, 9318, 27, 45, 63, 9018, 27, 54, 60, 9318, 27, 54, 63, 9018, 30, 42, 57, 6918, 30, 42, 57, 9618, 30, 42, 69, 7518, 30, 42, 75, 9618, 30, 45, 69, 7218, 30, 45, 72, 9618, 30, 54, 69, 7218, 30, 54, 72, 9618, 36, 42, 57, 9018, 36, 42, 75, 9018, 36, 45, 72, 9018, 36, 54, 72, 9018, 39, 42, 57, 6018, 39, 42, 60, 7518, 39, 45, 60, 7218, 39, 54, 60, 7218, 42, 57, 60, 9318, 42, 57, 63, 9018, 42, 60, 75, 9318, 42, 63, 75, 9018, 45, 60, 72, 9318, 45, 63, 72, 9018, 54, 60, 72, 9318, 54, 63, 72, 90 21, 30, 45, 69, 7821, 30, 45, 69, 8721, 30, 45, 78, 9621, 30, 45, 87, 9621, 30, 48, 57, 6921, 30, 48, 57, 9621, 30, 48, 69, 7521, 30, 48, 75, 9621, 30, 54, 69, 7821, 30, 54, 69, 8721, 30, 54, 78, 9621, 30, 54, 87, 9621, 30, 57, 69, 8421, 30, 57, 84, 9621, 30, 69, 75, 8421, 30, 75, 84, 9621, 36, 45, 78, 9021, 36, 45, 87, 9021, 36, 48, 57, 9021, 36, 48, 75, 9021, 36, 54, 78, 9021, 36, 54, 87, 9021, 36, 57, 84, 9021, 36, 75, 84, 9021, 39, 45, 60, 7821, 39, 45, 60, 8721, 39, 48, 57, 6021, 39, 48, 60, 7521, 39, 54, 60, 7821, 39, 54, 60, 8721, 39, 57, 60, 8421, 39, 60, 75, 8421, 45, 60, 78, 9321, 45, 60, 87, 9321, 45, 63, 78, 9021, 45, 63, 87, 9021, 48, 57, 60, 9321, 48, 57, 63, 9021, 48, 60, 75, 9321, 48, 63, 75, 9021, 54, 60, 78, 9321, 54, 60, 87, 9321, 54, 63, 78, 9021, 54, 63, 87, 9021, 57, 60, 84, 9321, 57, 63, 84, 9021, 60, 75, 84, 9321, 63, 75, 84, 9024, 30, 51, 69, 7824, 30, 51, 69, 8724, 30, 51, 78, 9624, 30, 51, 87, 9624, 30, 57, 69, 8124, 30, 57, 81, 9624, 30, 69, 75, 8124, 30, 75, 81, 9624, 36, 51, 78, 9024, 36, 51, 87, 9024, 36, 57, 81, 9024, 36, 75, 81, 9024, 39, 51, 60, 7824, 39, 51, 60, 8724, 39, 57, 60, 8124, 39, 60, 75, 8124, 51, 60, 78, 9324, 51, 60, 87, 9324, 51, 63, 78, 9024, 51, 63, 87, 9024, 57, 60, 81, 9324, 57, 63, 81, 9024, 60, 75, 81, 9324, 63, 75, 81, 90 27, 30, 45, 69, 8127, 30, 45, 81, 9627, 30, 48, 51, 6927, 30, 48, 51, 9627, 30, 51, 69, 8427, 30, 51, 84, 9627, 30, 54, 69, 8127, 30, 54, 81, 9627, 36, 45, 81, 9027, 36, 48, 51, 9027, 36, 51, 84, 9027, 36, 54, 81, 9027, 39, 45, 60, 8127, 39, 48, 51, 6027, 39, 51, 60, 8427, 39, 54, 60, 8127, 45, 60, 81, 9327, 45, 63, 81, 9027, 48, 51, 60, 9327, 48, 51, 63, 9027, 51, 60, 84, 9327, 51, 63, 84, 9027, 54, 60, 81, 9327, 54, 63, 81, 9030, 42, 51, 69, 7830, 42, 51, 69, 8730, 42, 51, 78, 9630, 42, 51, 87, 9630, 42, 57, 69, 8130, 42, 57, 81, 9630, 42, 69, 75, 8130, 42, 75, 81, 9630, 45, 69, 72, 8130, 45, 72, 81, 9630, 48, 51, 69, 7230, 48, 51, 72, 9630, 51, 69, 72, 8430, 51, 72, 84, 9630, 54, 69, 72, 8130, 54, 72, 81, 9636, 42, 51, 78, 9036, 42, 51, 87, 9036, 42, 57, 81, 9036, 42, 75, 81, 9036, 45, 72, 81, 9036, 48, 51, 72, 9036, 51, 72, 84, 9036, 54, 72, 81, 9039, 42, 51, 60, 7839, 42, 51, 60, 8739, 42, 57, 60, 8139, 42, 60, 75, 8139, 45, 60, 72, 8139, 48, 51, 60, 7239, 51, 60, 72, 8439, 54, 60, 72, 8142, 51, 60, 78, 9342, 51, 60, 87, 9342, 51, 63, 78, 9042, 51, 63, 87, 9042, 57, 60, 81, 9342, 57, 63, 81, 9042, 60, 75, 81, 9342, 63, 75, 81, 9045, 60, 72, 81, 9345, 63, 72, 81, 9048, 51, 60, 72, 9348, 51, 63, 72, 9051, 60, 72, 84, 9351, 63, 72, 84, 9054, 60, 72, 81, 9354, 63, 72, 81, 90

There are 288 different solutions.

Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon search box and some items chosen and recommended by Transum Mathematics to get you started.

The analytics show that more and more people are accessing Transum Mathematics via an iPad as it is so portable and responsive. The iPad has so many other uses in addition to solving Transum's puzzles and challenges and it would make an excellent gift for anyone.

The redesigned Retina display is as stunning to look at as it is to touch. It all comes with iOS, the world's most advanced mobile operating system. iPad Pro. Everything you want modern computing to be. more...

I had been tutoring the wonderful Betsy for five years. When the day came for our last ever session together before the end of her Year 13, I received this beautiful book as a gift of appreciation.

This a very readable book by Ben Orlin. I'm really enjoying the humour in the writing and the drawings are great.

Ben Orlin answers maths' three big questions: Why do I need to learn this? When am I ever going to use it? Why is it so hard? The answers come in various forms-cartoons, drawings, jokes, and the stories and insights of an empathetic teacher who believes that mathematics should belong to everyone.

 Teacher, do your students have access to computers?Do they have iPads or Laptops in Lessons? Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Transum.org/go/?Start=December2

Here is the URL which will take them to a related student activity.

Transum.org/go/?to=Hot

For Students:

For All: