Can you find digits to replace the letters to make this sum correct?
Note to teacher: If you are presenting this puzzle to your class using a projector you can slowly scroll down the step by step guide below giving clues that might enable your students to finish off the puzzle for themselves.
There is no standard way to solve a problem like this. Each one is quite different in structure and will have its own clues; but having said that here is an example of how to solve this particular challenge which may give you ideas for solving others.
We should assume that each letter stands for a different digit.
1. The first thing to notice is that the bottom line has six digits. When the two Ts are added together the answer caused a digit to be carried. This carried digit is most likely a one though there is a small possibility it could be a 2. Lets go with one and backtrack to here if it does not work out.
2. Looking at the tens column, to produce a digit one in the bottom line, the U must be a nine unless there is a digit carried from the units column. Lets go with nine and backtrack to here if it does not work out.
It may be useful to keep a record of the letters involved in the puzzle and the possible digits they could stand for:
3. Now it is a little more difficult to spot any certainties though we can see that if R is even then N is also even (and the inverse).
Let's make a guess and see how far it takes us. We'll start with the units column as there won't be any carried numbers to worry about.
Our guess for R will be the smallest digit it could possibly be, zero. If that is not correct and we get stuck further along we can always backtrack to this point and change our guess to the next smallest digit and so on.
If R is zero then N must be 2.
At this point be careful you don't get the letter O and the digit zero confused. We will use the slashed zero, Ø, to avoid confusion.
The table is updated with this information.
By working through the columns from right to left we can deal with the carried numbers as they appear.
4. Let's make another guess. This time for the letter O. We can see from the table that the smallest digit it could possibly be is a three. If that is not correct and we get stuck further along we can always backtrack to this point and change our guess to the next smallest digit and so on.
If O is 3 then V must be four as one is carried over from the 10s column.
The table is updated with this information.
5. Let's make another guess. This time for the letter H. We can see from the table that the smallest digit it could possibly be is a five.
If H is five, F would have to be one to produce the given column total but we have already assigned the digit one so H cannot be five. Let's backtrack.
We can see from the table that the next smallest digit it could possibly be is a six.
If H is six, F would have to be nine to produce the given column total but we have already assigned the digit nine so H cannot be six. Let's backtrack.
We can see from the table that the next smallest digit it could possibly be is a seven.
If H is seven, F would have to also be seven to produce the given column total but we cannot assign the same digit to two different letters. Let's backtrack.
We can see from the table that the only other possible choice for the letter H is eight.
If H is eight, F would have to be five:
The table is updated with this information.
6. Let's now guess the letter T. We can see from the table that the smallest digit it could possibly be is a six.
Two sixes with the two carried from the thousands column makes 14 but L cannot be four as that digit has already been assigned. Let's backtrack.
The only remaining possibility is that T is seven making L equal to six.
Here are some other solutions found by making different guesses in the process above. Can you find any others?
Here are some other word sums to try:
Finally here is the URL which will take you to a code cracking activity.
Christmas Present Ideas
It is often very difficult choosing Christmas presents for family and friends but so here are some seasonal, mathematics-related gifts chosen and recommended by Transum Mathematics.
Equate board game
Here's a great board game that will give any family with school-aged kids hours of worthwhile fun. Christmas is a time for board games but this one will still be useful at any time of year. Games can be adapted to suit many levels of Mathematical ability.
For Maths tutors working with just one or small groups of pupils this game has proved to be an excellent activity for a tutorial. Deciding on the best moves can spark pertinent discussions about mathematical concepts.
Equate looks a bit like Scrabble--for aspiring mathematicians, that is. Designed by a real mathematician, it works like this: You put down tiles on a board and make points by correctly completing simple equations. Your nine tiles include both numbers and mathematical symbols; you can add on to previous plays both vertically and horizontally. more...
How Not To Be Wrong
The maths we learn in school can seem like an abstract set of rules, laid down by the ancients and not to be questioned. In fact, Jordan Ellenberg shows us, maths touches on everything we do, and a little mathematical knowledge reveals the hidden structures that lie beneath the world's messy and chaotic surface. In How Not to be Wrong, Ellenberg explores the mathematician's method of analyzing life, from the everyday to the cosmic, showing us which numbers to defend, which ones to ignore, and when to change the equation entirely. Along the way, he explains calculus in a single page, describes Gödel's theorem using only one-syllable words, and reveals how early you actually need to get to the airport.
What more could the inquisitive adult want for Christmas? This book makes a cosy, interesting read in front of the fire on those cold winter evenings. more...
Graphic Display Calculator
This handheld device and companion software are designed to generate opportunities for classroom exploration and to promote greater understanding of core concepts in the mathematics and science classroom. TI-Nspire technology has been developed through sound classroom research which shows that "linked multiple representation are crucial in development of conceptual understanding and it is feasible only through use of a technology such as TI-Nspire, which provides simultaneous, dynamically linked representations of graphs, equations, data, and verbal explanations, such that a change in one representation is immediately reflected in the others.
For the young people in your life it is a great investment. Bought as a Christmas present but useful for many years to come as the young person turns into an A-level candidate then works their way through university. more...
Apple iPad Pro
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...
Before giving an iPad as a Christmas gift you could add a link to iPad Maths to the home screen.
Aristotle's Number Puzzle
It’s a bit of a tradition to give puzzles as Christmas Gifts to nieces and nephews. This puzzle is ideal for the keen puzzle solver who would like a challenge that will continue over the festive period (at least!).
This number puzzle involves nineteen numbers arranged into a hexagon. The goal of the puzzle is to rearrange the numbers so each of the fifteen rows add up to 38. It comes in a wooden style with an antique, aged look.
Keep the Maths in Christmaths with this reasonably priced stocking filler. more...
The Story Of Maths [DVD]
The films in this ambitious series offer clear, accessible explanations of important mathematical ideas but are also packed with engaging anecdotes, fascinating biographical details, and pivotal episodes in the lives of the great mathematicians. Engaging, enlightening and entertaining, the series gives viewers new and often surprising insights into the central importance of mathematics, establishing this discipline to be one of humanity s greatest cultural achievements. This DVD contains all four programmes from the BBC series.
Marcus du Sautoy's wonderful programmes make a perfect Christmas gift more...
This book provides a wealth of fun activities with a Christmas theme. Each photocopiable worksheet is matched to the Numeracy Strategy and compatible with the Scottish 5-14 Guidelines. This series is designed for busy teachers in the late Autumn term who are desperate for materials that are relevant and interesting and that can be completed with minimun supervision.
All the activities are suitable for use by class teachers, supply teachers, SEN teachers and classroom assistants and cover topics such as 'How many partridges did the true love give all together?' and 'Filling a sleigh with presents by rolling a dice!'. Children will have lots of fun working through the Christmas Maths themes but also gain valuable skills along the way.
A great source of ideas and another reasonably priced stocking filler. more...
Click the images above to see all the details of these gift ideas and to buy them online.
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.
Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.