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#### Resources tagged with Place value similar to Weekly Problem 33 - 2011:

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### There are 66 results

Broad Topics > Numbers and the Number System > Place value

### Seven Up

##### Stage: 3 Challenge Level:

The number 27 is special because it is three times the sum of its digits 27 = 3 (2 + 7). Find some two digit numbers that are SEVEN times the sum of their digits (seven-up numbers)?

### Chocolate Maths

##### Stage: 3 Challenge Level:

Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .

### Quick Times

##### Stage: 3 Challenge Level:

32 x 38 = 30 x 40 + 2 x 8; 34 x 36 = 30 x 40 + 4 x 6; 56 x 54 = 50 x 60 + 6 x 4; 73 x 77 = 70 x 80 + 3 x 7 Verify and generalise if possible.

### Always a Multiple?

##### Stage: 3 Challenge Level:

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

### How Many Miles to Go?

##### Stage: 3 Challenge Level:

A car's milometer reads 4631 miles and the trip meter has 173.3 on it. How many more miles must the car travel before the two numbers contain the same digits in the same order?

### Mini-max

##### Stage: 3 Challenge Level:

Consider all two digit numbers (10, 11, . . . ,99). In writing down all these numbers, which digits occur least often, and which occur most often ? What about three digit numbers, four digit numbers. . . .

### Legs Eleven

##### Stage: 3 Challenge Level:

Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?

### Eleven

##### Stage: 3 Challenge Level:

Replace each letter with a digit to make this addition correct.

### Repeaters

##### Stage: 3 Challenge Level:

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

### Three Times Seven

##### Stage: 3 Challenge Level:

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

### Reverse to Order

##### Stage: 3 Challenge Level:

Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?

### Tis Unique

##### Stage: 3 Challenge Level:

This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

### Cycle It

##### Stage: 3 Challenge Level:

Carry out cyclic permutations of nine digit numbers containing the digits from 1 to 9 (until you get back to the first number). Prove that whatever number you choose, they will add to the same total.

### Two and Two

##### Stage: 2 and 3 Challenge Level:

How many solutions can you find to this sum? Each of the different letters stands for a different number.

### Power Mad!

##### Stage: 3 Challenge Level:

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

### Basically

##### Stage: 3 Challenge Level:

The number 3723(in base 10) is written as 123 in another base. What is that base?

### What an Odd Fact(or)

##### Stage: 3 Challenge Level:

Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?

### Pupils' Recording or Pupils Recording

##### Stage: 1, 2 and 3

This article, written for teachers, looks at the different kinds of recordings encountered in Primary Mathematics lessons and the importance of not jumping to conclusions!

### What Do You Need?

##### Stage: 2 Challenge Level:

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

### Skeleton

##### Stage: 3 Challenge Level:

Amazing as it may seem the three fives remaining in the following `skeleton' are sufficient to reconstruct the entire long division sum.

### Just Repeat

##### Stage: 3 Challenge Level:

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

### Trebling

##### Stage: 2 Challenge Level:

Can you replace the letters with numbers? Is there only one solution in each case?

### Football Sum

##### Stage: 3 Challenge Level:

Find the values of the nine letters in the sum: FOOT + BALL = GAME

### Cayley

##### Stage: 3 Challenge Level:

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

### Six Times Five

##### Stage: 3 Challenge Level:

How many six digit numbers are there which DO NOT contain a 5?

### Back to the Planet of Vuvv

##### Stage: 3 Challenge Level:

There are two forms of counting on Vuvv - Zios count in base 3 and Zepts count in base 7. One day four of these creatures, two Zios and two Zepts, sat on the summit of a hill to count the legs of. . . .

### Double Digit

##### Stage: 3 Challenge Level:

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. . . .

### (w)holy Numbers

##### Stage: 2 Challenge Level:

A church hymn book contains 700 hymns. The numbers of the hymns are displayed by combining special small single-digit boards. What is the minimum number of small boards that is needed?

### Oddly

##### Stage: 2 Challenge Level:

Find the sum of all three-digit numbers each of whose digits is odd.

### Permute It

##### Stage: 3 Challenge Level:

Take the numbers 1, 2, 3, 4 and 5 and imagine them written down in every possible order to give 5 digit numbers. Find the sum of the resulting numbers.

### Spell by Numbers

##### Stage: 2 Challenge Level:

Can you substitute numbers for the letters in these sums?

### ABC

##### Stage: 2 Challenge Level:

In the multiplication sum, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

### Adding with the Abacus

##### Stage: 1, 2, 3 and 4

Nowadays the calculator is very familiar to many of us. What did people do to save time working out more difficult problems before the calculator existed?

### Diagonal Sums

##### Stage: 2 Challenge Level:

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

### One Million to Seven

##### Stage: 2 Challenge Level:

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

### The Thousands Game

##### Stage: 2 Challenge Level:

Each child in Class 3 took four numbers out of the bag. Who had made the highest even number?

### Reach 100

##### Stage: 2 Challenge Level:

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

### Balance Power

##### Stage: 3, 4 and 5 Challenge Level:

Using balancing scales what is the least number of weights needed to weigh all integer masses from 1 to 1000? Placing some of the weights in the same pan as the object how many are needed?

### Coded Hundred Square

##### Stage: 2 Challenge Level:

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

### Snail One Hundred

##### Stage: 1 and 2 Challenge Level:

This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.

### Lesser Digits

##### Stage: 3 Challenge Level:

How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?

### Light the Lights

##### Stage: 2 Challenge Level:

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

### Dicey Operations

##### Stage: 2 and 3 Challenge Level:

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

### Some Games That May Be Nice or Nasty

##### Stage: 2 and 3 Challenge Level:

There are nasty versions of this dice game but we'll start with the nice ones...

### Napier's Bones

##### Stage: 2 Challenge Level:

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

### Six Is the Sum

##### Stage: 2 Challenge Level:

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

### Not a Polite Question

##### Stage: 3 Challenge Level:

When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...

### Calculator Bingo

##### Stage: 2 Challenge Level:

A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.

### Learn about Number Bases

##### Stage: 3, 4 and 5

We are used to writing numbers in base ten, using 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Eg. 75 means 7 tens and five units. This article explains how numbers can be written in any number base.

### X Marks the Spot

##### Stage: 3 Challenge Level:

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .
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