Transcript The Problem - Maths Tallis

MATHEMATICAL PUZZLE
STARTERS
Taken from http://7puzzleblog.com/
The Problem
You must arrive at the answer of 7 by using the formula
(a x b) ± c,
where a b c are three unique digits from 2-9.
If (5 x 2) – 3 = 7, list the other FOUR ways of making 7,
keeping to the above rules.
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The Problem
Using the numbers 3 5 5 once each, with + – x ÷available, which
FOUR numbers from the following list are NOT mathematically
possible to make:
1 4 7 10 13 15 18 20 22 25 28 30
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The Problem
List the THREE ways of making 36 when adding together six
unique digits from 1-9?
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The Problem
Insert + – x or ÷ each time you see ? so the result of each of
these 4-number calculations, when working one step at a time
from Left to Right (and no brackets allowed), is 28:
6 ? 5 ? 9 ? 8 = 28
8 ? 5 ? 5 ? 7 = 28
8 ? 6 ? 8 ? 2 = 28
6 ? 7 ? 2 ? 2 = 28
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The Problem
Insert + – x or ÷ each time you see ? so the result of each of
these 4-number calculations, when working one step at a time
from Left to Right (with no brackets), is 21 every time:
6 ? 5 ? 2 ? 1 = 21
4 ? 3 ? 1 ? 3 = 21
7 ? 2 ? 3 ? 2 = 21
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The Problem
Replace the 12 letters shown below with 0, 1, 2, 2, 3, 3, 4, 6, 6,
7, 9, 9 so all three lines work out:
A+B
E+F
I+J
= 6 = C - D
= 18 = G x H
= 3 = K÷L
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The Problem
You have the same starting number and final answer, both 32,
with lots of arithmetical steps in between, but the 10th step is
missing! What should it be?
Start with the number 32, then:
-5 ÷9 +4 x3 -3 ÷2 x5 -5 ÷2 ? x2 +4 ÷3 x2 = 32
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The Problem
You have the same starting number and final answer, both 22,
with lots of arithmetical steps in between, but the 10th and
final step is missing! What should it be?
Start with the number 22, then:
+2
÷6
x4
-3
x2 +4
÷5
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+5
x2
?
=
22
The Problem
Apart from 9+8+7+1, list the FIVE other ways of making 25
when adding together 4 UNIQUE digits from 1-9?
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The Problem
Which is the ONLY way of making 16 when adding together 5
unique digits from 1-9?
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The Problem
Playing a typical game of darts on a normal dartboard, you
need 92 to win the game, but have just TWO darts left. Apart
from TREBLE 20 DOUBLE 16, which are the other TWO ways
you can end the match?
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Problem 1
Add together:
• the months in six years
• the days in February (non-leap year)
• the minutes in three hours
• the seconds in five minutes
What is your total answer?
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The Problem
Using the numbers 3 5 6 once each, and with + – x ÷ available,
which target answers from 1-9 are NOT mathematically
possible to achieve?
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The Problem
Analyse the first three sets of numbers to find the value of ?
in the fourth set:
6-8-5 = 9 / 6-7-8 = 5 / 7-8-9 = 6 / 7-1-3 = ?
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The Problem
Which is the ONLY way of making 39 when adding together 6
unique digits from 1-9?
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The Problem
After analysing the first three sets of numbers, find the value
of ? in the fourth set:
1-2-3 = 5 / 2-3-4 = 8 / 4-5-6 = 14 / 10-11-12 = ?
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The Problem
What is the next number in the sequence, and why?
283 284 142 71 72 36 18 9 ?
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The Problem
You have been given a starting number and must arrive at the
same final answer, both 18, with lots of arithmetical steps in
between, but the 9th and penultimate step is missing! What
should it be?
Starting at 18:
÷2
+3
-8
x6
+4
-3
÷5
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x2
?
x3
=
18
Problem 1
Insert + – x or ÷ each time you see ? so the
result of each of the 4-number calculations
shown below is 38 when working one step at
a time from Left to Right (no brackets):
7
2
6
8
?
?
?
?
8
9
4
2
?
?
?
?
9
3
9
8
?
?
?
?
9
5
2
6
=
=
=
=
38
38
38
38
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The Problem
Insert + – x or ÷ each time you see ? below, so the result of
this 4-number calculation is 29. You must work one step at a
time from Left to Right (and no brackets allowed).
2 ? 3 ? 5 ? 4 = 29
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The Problem
One way of arriving at 31 by adding 5 unique digits is
9+8+7+6+1. Can you find the other FOUR ways of making
31 when adding together 5 unique digits from 1-9?
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The Problem
You have to make 9 when adding together either 2 or 3 unique
digits from 1-9. There are just SEVEN ways to do this, can you
list them?
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Problem 2
Each flavoured Gem represents a number
from 1 to 9. Can you discover the value of
each Gem, then find the total of the 5th row?
LEMON + PURPLE + WHITE = 15
LEMON + LEMON + WHITE
= 16
PURPLE + LEMON + PURPLE = 10
WHITE + WHITE + WHITE
= 24
WHITE + WHITE + PURPLE = ?
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The Problem
Your task is to make 8 when adding together either 2 or 3
unique digits from 1-9. There are just FIVE possible ways of
doing this, can you list them?
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The Problem
You must arrive at the target answer of 18 by using each of
the four numbers 2, 6, 7, 10 exactly once each and having +
– x ÷ available.
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The Problem
After analysing the first three sets of numbers, find the value
of ? in the fourth set:
6-2-9 = 3 / 7-1-3 = 4 / 4-2-7 = 1 / 4-3-6 = ?
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The Problem
Tyson, Usain and Johan were friends who were taking part in a
race. They finished first, second and third and wore yellow,
red and blue, but can you work out which position they each
came and the colour shirt they wore from these two clues:
• Johan did not win and wasn’t wearing blue
• Tyson wore red and overtook the person who was in second
place just before the line
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The Problem
You must visit every square below, just once each, starting at 1
and finishing at 49 by inserting the missing numbers from 149. When moving from number to number, you can move just
one square at a time in any direction, including diagonally.
x
13
x
x
x
x
5
x
x
18
x
x
x
x
16
48
x
x
20
9
x
45
x
49
x
x
1
2
x
43
x
x
x
23
x
37
x
39
33
31
x
x
x
35
x
x
29
27
x
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The Problem
We had a palindromic date earlier this year in the UK, namely
21 February 2012, written as 21.02.2012.
When is the next one due, if the date is represented in the
exact same format of 8 digits (dd.mm.yyyy)?
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The Problem
Replace the 12 letters shown below with 0, 1, 1, 2, 2, 3, 4, 5, 6,
7, 8, 9 so all three lines work out perfectly:
A+B
E+F
I+J
= 1 = C - D
= 12 = G x H
= 3 = K÷L
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The Problem
You must arrive at the answer of 42 by using the formula
(a x b) ± c,
where a b c are three unique digits from 0-9.
One way of making 42 is (9 x 4) + 6, so can you find the other
THREE?
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The Problem
Your task is to achieve 32 when receiving your card of three
numbers. You must use each number once, with + – x ÷
available. An example of two cards that would allow you to get
32 are:
Card 1 – 2 5 6 as (5 x 6) + 2 = 32
Card 2 – 4 4 4 as (4 + 4) x 4 = 32
List THREE other cards which would enable you to arrive at
32. Remember, the range of numbers on each card are 1-6.
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The Problem
Replace the 12 letters shown below with 0, 1, 1, 2, 2, 3, 4, 5, 5,
8, 9, 9, so all three lines work out:
A+B
E+F
I+J
= 3
= 8
= 1
=
=
=
C - D
GxH
K÷L
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The Problem
From each of the three groups of numbers below, you must
arrive at the target answer of 25 by using the four digits
exactly once each, and with + – x ÷ available:
3, 3, 4, 4
5, 7, 7, 9
2, 6, 7, 8
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The Problem
As there’s just 28 days to the start of the Olympic Games,
you must arrive at the answer of 28 by using the formula
(a x b) ± c,
where a b c are three unique digits from 1-9.
One way is (6 x 5) – 2 = 28, can you find the other FOUR
ways?
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The Problem
Replace the 12 letters shown below with 0, 1, 1, 2, 3, 4, 5, 5, 6,
7, 9, 9 so all three lines work out:
A+B
E+F
I+J
= 4 = C - D
= 18 = G x H
= 7 = K÷L
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The Problem
Insert + – x or ÷ when you see ? so the result of each of the
three 4-number calculations will equal 18 when you work one
step at a time from Left to Right (no brackets):
8 ? 4 ? 7 ? 4 = 18
4 ? 6 ? 4 ? 3 = 18
5 ? 2 ? 8 ? 2 = 18
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The Problem
Try and arrive at the target answer of 24 by using each of the
numbers 1, 4, 6, 9 exactly once each, with + – x ÷ available.
Extension Problem
As above, make 24 by using each of the numbers 1 3 6 9
exactly once each.
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The Problem
Using the numbers 4, 8, 12 once each, with + – x ÷ available,
which numbers from 1-30 are mathematically possible to
achieve?
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The Problem
In the 2008 Beijing Olympics, the host country, China, and the
United States were the top two countries in the official
Medals Table, as shown below:
China – 51 Gold; 21 Silver; 28 Bronze
USA – 36 Gold; 38 Silver; 36 Bronze
In our own 7puzzle Olympic Medals Table, we awarded 3
points for every Gold, 2 points for a Silver and 1 point for
a Bronze. Using our scoring system, which country would
top the table and by how many points?
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The Problem
1896 was the year of the first modern Olympic Games in
Athens. Since then, the Olympics have been held every four
years, except 1916 1940 and 1944 when they were cancelled
due to World Wars I and II. How many have therefore taken
place prior to the Games of the XXXth Olympiad in London?
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The Problem
Your task is to make a list of 2-digit numbers, in ascending
order, which does not contain any multiples of 4, 5 or 6, nor
any prime numbers, square numbers or cube numbers. What is
the 7th number in your list?
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The Problem
At a child’s birthday party, there are four mothers each with
one child. The four children are aged 1, 2, 3 and 4. Read these
seven facts:
•
•
•
•
•
•
•
•
It is Prue’s child’s birthday party
Millie is not the oldest child
Sue had Lily 18 months ago
Lou’s child will be 3 next birthday
Billy is older than Tilly
Koo’s child is the oldest
Tilly is older than Lou’s child
Who’s child is whose, and how old is each child?
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The Problem
At a child’s birthday party, there are four mothers each with
one child. The four children are aged 1, 2, 3 and 4. Read these
seven facts:
•
•
•
•
•
•
•
•
It is Prue’s child’s birthday party
Millie is not the oldest child
Sue had Lily 18 months ago
Lou’s child will be 3 next birthday
Billy is older than Tilly
Koo’s child is the oldest
Tilly is older than Lou’s child
Who’s child is whose, and how old is each child?
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The Problem
Time is dragging by at work for Jimmy. At noon, he looks over
at the clock on the wall. The big hand is on the seven while the
little hand is between the four and the five. What time is it?
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The Problem
There were 30 groups of golfers taking part in the final day of
a tournament and an 11-minute gap between each group’s
official starting time from the 1st tee. If the first group teed
off at 9.30am, what time did the last group tee off?
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The Problem
Try and arrive at the target answer of 7 by using each of the
numbers 7, 7, 7, 7 exactly once each, with + – x ÷ available.
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The Problem
Add together:
•
•
•
•
the 7th Prime number
the 7th Square number
the 7th 2-digit number
the 7th whole number that contains a ’7′
What is your answer?
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The Problem
Try and arrive at the target answer of 24 by using each of the
numbers 5, 7, 8, 8 exactly once each, with + – x ÷ available.
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The Problem
Find the first seven EVEN numbers that are not multiples
of 3, 5 or 7. What is the 7th number in your list?
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The Problem
Starting from 1, add together the first SEVEN ODD numbers
that do not contain a 3, 5 or 7 as part of their number, or are
not divisible by 3, 5 or 7. What is your answer?
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The Problem
What is the sum of the 1st 100 whole numbers, that is 1 + 2 +
3 + 4 + . . . + 99 + 100?
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The Problem
Find the first SEVEN whole numbers, above 20, that do not
contain a 3, 5 or 7 as part of their number, or are not
multiples of 3, 5 or 7. What is the 7th number in your list?
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The Problem
You must arrive at the answer of 10 by using the formula
(a x b) ± c,
where a, b, c are three unique digits from 2-9.
If (4 x 3) – 2 = 10, list the other FIVE ways of making 10,
keeping to the above rules.
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The Problem
Replace the 12 letters shown below with 1, 1, 2, 2, 3, 3, 4, 4, 5,
6, 7, 8 so all three lines work out:
A+B
E+F
I+J
= 5 = C - D
= 9 = GxH
= 8 = K÷L
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The Problem
Insert + – x or ÷ each time you see ? so the result of each of
these 5-number calculations, when working one step at a time
from Left to Right (with no brackets), is 23 in each case:
3 ? 3 ? 3 ? 3 ? 1 = 23
4 ? 4 ? 4 ? 4 ? 3 = 23
5 ? 5 ? 5 ? 5 ? 2 = 23
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The Problem
After looking at the first three sets of numbers, find the
value of ? in the fourth set:
6-2-2 = 8 / 7-3-5 = 6 / 7-2-4 = 6 / 6-3-5 = ?
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The Problem
As there’s just 39 days to the start of the Olympic Games,
you must arrive at the answer of 39 by using the formula
(a x b) ± c,
where a, b, c are three unique digits from 1-9.
One way of getting there is (6 x 5) + 9; can you find the other
SEVEN ways?
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The Problem
You notice, when stopping at a petrol station, that the reading
on your car’s dashboard is a palindrome as it has travelled
15951 miles in total.
How many more miles must you drive until the reading becomes
another palindromic number?
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The Problem
On a normal dartboard, you need to score 69 to win the game,
but have just TWO darts left. Apart from TREBLE 11 DOUBLE
18, show the other FIVE ways can you do this when ending a
typical darts match in the proper manner.
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The Problem
Replace the 12 letters shown below with 0, 1, 1, 2, 2, 3, 3, 4, 6,
6, 7, 7 so all three lines work out:
A+B
E+F
I+J
= 2 = C - D
= 9 = GxH
= 7 = K÷L
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The Problem
Your task is to arrive at the target answer of 24 by using each
of the numbers 2, 3, 7, 9 exactly once each and having + – x ÷
available.
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The Problem
Your task is to arrive at the target answer of 24 by using each
of the four numbers 0.5, 1, 5, 10 exactly once each and
having + – x ÷ available.
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The Problem
You must arrive at the answer of 37 by using the formula
(a x b) ± c,
where a b c are three unique digits from 1-9.
One way of achieving this is (7 x 5) + 2, you must find the
other SEVEN ways.
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The Problem
Starting from 1, find the total of the first SEVEN whole
numbers that do not contain a 3, 5 or 7 as part of their
number, or are not multiples of 3, 5 or 7.
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The Problem
Imagine to win the game, you had to achieve 30 when receiving
your card. You must use each number once, with + – x ÷
available. An example of two cards that would allow you to
make 30 are:
Card 1 – 1 5 6 as (5 x 6) x 1 = 30
Card 2 – 4 6 6 as (6 x 4) + 6 = 30
Can you list at least FIVE other cards that would enable you to
arrive at 30 and win the game?
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The Problem
Replace the letters A B C D and E with the digits 1 2 3 4 and 5
so that the following equation works:
AB x C = DE
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The Problem
Using ALL six numbers 8, 12, 19, 19, 20, 48 once each, and with
+ – x ÷ available, today’s task is to arrive at the target answer
of 432.
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The Problem
Insert + – x or ÷ each time you see ? so the result of this 6number calculation is 39 when working one step at a time from
Left to Right (with no brackets):
3 ? 9 ? 3 ? 9 ? 3 ? 9 = 39
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The Problem
Using ALL six numbers 8, 12, 19, 19, 20, 48 once each, and with
+ – x ÷ available, try and arrive at the target answer of 408.
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The Problem
List SEVEN numbers that total 101, but:
• each number must be at least 4 away from one another
• the list must contain THREE square numbers
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The Problem
Insert + – x or ÷ each time you see ? so the result of this 12number calculation is 36. You must work one step at a time
from Left to Right (and no brackets allowed) and all four
operations have to be used:
1 ? 3 ? 5 ? 7 ? 9 ? 2 ? 4 ? 6 ? 8 ? 8 ? 3 ? 6 = 36
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The Problem
You have a 6-sector dartboard containing the numbers 16, 17,
23, 24, 39, 40.
Using some darts, your task is to achieve a score of EXACTLY
100 when adding your scores together. You can throw as many
darts as you want and they can land in each sector more than
once.
There is only ONE way of achieving 100. How can it be done?
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The Problem
You must arrive at the answer of 23 by using the formula
(a x b) ± c,
where a b c are three unique digits from 1-9.
If (7 x 2) + 9 is one such way of making 23, how many
different ways are there in all?
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The Problem
Insert + – x or ÷ each time you see ? so the result of this 7number calculation is 35. You must work one step at a time
from Left to Right (and no brackets allowed):
6 ? 2 ? 7 ? 9 ? 5 ? 3 ? 8 = 35
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The Problem
Insert + – x or ÷ each time you see ? below, so the result of
the 7-number calculation is 30. You must work one step at a
time from Left to Right (and no brackets allowed).
To really test the puzzle enthusiasts, all four arithmetical
operations must be used at some point in the calculation below:
4 ? 1 ? 7 ? 6 ? 2 ? 2 ? 1 = 30
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The Problem
Insert + – or x each time you see ? so the result of this 7number calculation is 25. You must work one step at a time
from Left to Right (and no brackets allowed):
1 ? 2 ? 3 ? 4 ? 5 ? 6 ? 7 = 25
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The Problem
Insert + – x or ÷ each time you see ? so the result of this 7number calculation is 15. You must work one step at a time
from Left to Right (with no brackets) and all four arithmetical
operations shown above must be used at some point:
7 ? 2 ? 5 ? 1 ? 4 ? 6 ? 3 = 15
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The Problem
Try and arrive at the target answer of 24 by using each of the
numbers 2, 4, 4, 5 exactly once each, with + – x ÷ available
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The Problem
You must arrive at the target answer of 32 by
using 2, 8, 8, 9 exactly once each and having + – x ÷
available.
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The Problem
After analysing the first three sets of numbers, find the values of
x and y in the fourth and fifth sets:
7-2-3 = 13 / 6-3-7 = 8 / 3-5-5 = 6 / 5-1-7 = x / 8-y-10 = 15
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The Problem
You must arrive at the target answer of 24 by
using 1.5 2 2.5 4.5 exactly once each and having + – x ÷ available
to you.
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The Problem
Try and arrive at the target answer of 24 by using each of the
numbers 1, 3, 8, 8 exactly once each, with + – x ÷ available.
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The Problem
Using the numbers 4, 5, 6 once each, with + – x ÷ available, which
target numbers from 1-30 is it mathematically possible to
achieve?
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The Problem
Insert + – x or ÷ each time you see ? so the end result of this 7number calculation is 10. You must work one step at a time from
Left to Right (with no brackets), and all four arithmetical
operations shown above must be used at some point in your answer:
1 ? 2 ? 3 ? 4 ? 5 ? 6 ? 7 = 10
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The Problem
Replace the 16 letters below with digits from 0-9. Can you make all
four lines work out if the digits inserted can only be used a
maximum of TWICE each?
A + B = 12
E+F = 1
I+J = 9
M+N = 2
= C+D
= G–H
= KxL
= P÷R
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The Problem
Your task is to arrive at the target answer of 24 by using each of
the numbers 2, 2, 6, 9 exactly once each and having + – x ÷
available. Can you do it?
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The Problem
The rule for a sequence of numbers is:
• if EVEN, halve it
• if ODD, subtract 1
So, if starting at 50, the sequence would be 50, 25, 24, 12, 6, 3, 2,
1, thus taking 7 steps to get from 50 down to 1.
Following the above rules, which starting number between 50
and 100 would give you the most amount of steps when
eventually arriving at 1?
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The Problem
Insert + – x or ÷ each time you see ? so the result of this 7number calculation is 31. You must work one step at a time from
Left to Right (and no brackets allowed):
7 ? 3 ? 9 ? 6 ? 5 ? 3 ? 6 = 31
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The Problem
Insert + – x or ÷ each time you see ? so the result of this 7number calculation is 22 when working one step at a time, from
Left to Right (with no brackets), and using ALL four operations in
your calculation:
1 ? 2 ? 3 ? 4 ? 5 ? 6 ? 7 = 22
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The Problem
Insert + – x or ÷ each time you see ? so the result of this 7number calculation is 37 when working one step at a time from
Left to Right (with no brackets):
2 ? 9 ? 6 ? 3 ? 2 ? 4 ? 5 = 37
You MUST use all four arithmetical operations in your answer!
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The Problem
Insert + – x or ÷ each time you see ? so the result of this 7number calculation is 41 when working one step at a time from
Left to Right (with no brackets).
To add a little extra spice to this particular question, ALL four
arithmetical operations must be used:
8 ? 4 ? 5 ? 6 ? 9 ? 8 ? 7 = 41
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The Problem
You are taking part in the Olympic 800 metres Final. As the race
nears the halfway point, you suddenly accelerate and overtake the
runner who was in 2nd place. What position are you in now?
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The Problem
A boat floats in the harbour at low tide. A ladder is fixed to the
side of the boat, and seven rungs of the ladder are showing above
the waterline.
If the rungs are 25cm apart and the sea level rises at a rate of
40cm per hour, how many rungs will be showing above water after
three hours?
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The Problem
Using ALL six numbers 19, 08, 19, 48, 20, 12 once each, and with +
– x ÷ available, your task is to arrive at the target answer of 456.
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The Problem
When replacing the 16 letters below with digits from 0-9, each
digit can only be used a maximum of TWICE. Can you make all four
lines work out perfectly?
A+B =
E+F =
I+J =
M+N =
16
6
10
9
=
=
=
=
C+D
G–H
KxL
P÷R
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The Problem
Replace the 16 letters shown below with 0, 0, 1, 1, 2, 2, 4, 4, 5, 5,
6, 6, 7, 7, 8, 9 so that the four lines work out:
A + B = 15
E+F = 2
I+J = 8
M+N = 1
=
=
=
=
C+D
G–H
KxL
P÷R
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The Problem
Using ALL six numbers 8, 12, 19, 19, 20, 48 once each, and with + –
x ÷ available, can you arrive at the target answer of 480?
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The Problem
Replace the 16 letters shown below with 0, 1, 1, 2, 2, 3, 3, 4, 4, 5,
5, 6, 6, 7, 8, 8 so that the four lines work out:
A+B =
E+F =
I+J =
M+N =
12 =
5 =
10 =
2 =
C+D
G–H
KxL
P÷R
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The Problem
Replace the 16 letters shown below with 0, 0, 1, 1, 2, 2, 3, 4, 4, 5,
6, 7, 7, 8, 9, 9 so that the four lines work out:
A+B = 9
E+F = 7
I + J = 12
M+N = 6
=
=
=
=
C+D
G–H
KxL
P÷R
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The Problem
Imagine receiving three different cards which each contain three
numbers as shown below:
Card 1 – 2 6 10
Card 2 – 3 7 10
Card 3 – 4 8 10
For each card, use the numbers once each. With + – x ÷ available,
find which target answers from 1-30 are common to ALL three
cards.
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