Global Math Challenge | Sample
01 Which is the Lightest Animal? Question
There are four kinds of stuffed animals–a pig, a cat, a rabbit, and a bear. They are placed on balance scales as shown below. Which one is the lightest of the four?
1
Pig
2
Cat
2
Cat.
3
Rabbit
4
Bear
Answer
The answer is
Go to the explanation!
1
Global Math Challenge | Sample
01 Explanation a. a
Rabbit
Cat
Pig Bear
Label each picture as [a], [b], [c].
ｂ
c
Put animals of the same weight on both sides of the scale.
Step ① Compare [a] with [b]. a
(balanced) same weight
a.
The pointer on the scale does not move, as animals of the same weight were added.
Put them on scale [b].
ｂ
lighter
ｂ-1
heavier
Remove the animals which are on both sides of the scale.
lighter
is lighter than
heavier
making their exit
,
making their exit
Move on! 2
Global Math Challenge | Sample
01 Explanation a
(balanced) same weight
a.
Next, put these animals on the other side of scale [b].
ｂ-2 lighter
is lighter than
heavier
,
Step ② Compare [a] with [c].
a
same weight
a.
Put them on scale [c] and compare!
c -1
heavier
lighter
is lighter than
,
Move on! 3
Global Math Challenge | Sample
01 Explanation a
same weight
a.
Next, put these animals on the other sides of scale [c].
c -2 lighter
heavier
is lighter than
,
Result Which is the lightest? As in steps ① and ②, the relation between the animals in weight is as follows... Step①
lighter
heavier
lighter
heavier
Step②
Therefore, the answer is:
The cat is the lightest.
4
Global Math Challenge | Sample
02 4-Digit Password Question
Joey had totally forgotten the password for his cell phone. He tried to remember the number.
After missing out all five tries, he finally nailed it at the sixth shot. He found out that every guess he made included two correct digits, although they were not put in the correct places. What is the four digit code needed to unlock the phone?
Answer
The answer is 8712. Go to the explanation! 5
Global Math Challenge | Sample
02 Explanation 1st try
4th try Was it
6 0 8 7
Wait! How about...
?
5th try
2nd try No? Well, then...
5 1 7 3
?
3 8 2 5
?
Enter Password
This can’t be true... Ah, yes! Must be
2 5 3 1
!!
3rd try
1
2
3
4
5
6
7
8
9
0 Seriously? OK, try
1 3 5 8
!!
Step ① What numbers are not used for the password? Question
After missing out on all five tries, he finally nailed it at the sixth shot. He found out that every guess he made included two correct digits, although they were not put in the correct places. Read the question carefully and let’s put it in a simpler way. Joey’s 1st try
6
0
8
7
2nd try
5
1
7
3
3rd try
1
3
5
8
4th try
3
8
2
5
5th try
2
5
3
1
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
All the numbers Joey used were put in the wrong places - so we can’t use numbers in their original position.
Not used in any place!
6
Move on!
Global Math Challenge | Sample
02 Explanation Step ② What numbers are used for the password?
According to Step ①, let's exclude 3 & 5. They aren’t used at all.
Joey’s 1st try
6 0 8 7
2nd try
5 1 7 3
3rd try
1 3 5 8
4th try
3 8 2 5
5th try
2 5 3 1
Since "every guess he made included two correct digits",
1, 2, 7, 8 are definitely in!
Step ③ Arrange the four digits to discover the password.
Now it's time to decide the order of 1, 2, 7, 8. Remember that each digit cannot be put in the place that Joey originally tried. Let's look at each digit one by one.
I.
Where does 1 go? Joey’s 1st try
6 0 8 7
2nd try
5 1 7 3
3rd try
1 3 5 8
4th try
3 8 2 5
5th try
2 5 3 1
Only fits here!
1
Move on! 7
Global Math Challenge | Sample
02 Explanation II.
Where does 2 go?
Joey’s 1st try
III.
6 0 8 7
2nd try
5 1 7 3
3rd try
1 3 5 8
4th try
3 8 2 5
5th try
2 5 3 1
2
2
Where does 7 go?
Joey’s 1st try
6 0 8 7
2nd try
5 1 7 3
3rd try
1 3 5 8
4th try
3 8 2 5
5th try
2 5 3 1
IV.
Either of these.
Either of these.
7 7
Where does 8 go?
Joey’s 1st try
6 0 8 7
2nd try
5 1 7 3
3rd try
1 3 5 8
4th try
3 8 2 5
5th try
2 5 3 1
Only fits here!
8
Move on! 8
Global Math Challenge | Sample
02 Explanation Now, you can work out the position for 7.
Fixed digits
8
1
Which place is for 7?
7 7
7 7 HERE!
Finally, you can work out the position for 2!
Fixed digits
8 7 1
Where does 2 go?
2
2
2
2 HERE!
Result According to Steps ①, ② & ③,
8
the four digit password is
9
7
1
2
.
Global Math Challenge | Sample
03 Five Sets of Rings Question
We assemble five sets of jump rings into a linked circle as shown below.
The rules to assemble rings are as follows:
It costs $1 to cut open a ring.
It costs $2 to weld a ring closed.
What is the lowest fee to make it?
Answer
The answer is $12.
Go to the explanation!
10
Global Math Challenge | Sample
03 Explanation
Step① Cut open one ring from each set and join it to the next set!
Let's give them 5 different colors! It looks much clearer. a
c
b
e
d
a
5
e
1
b
d
2
weld
open 4
c
Since it costs $1 to cut open
3 and $2 to weld
A pair of one "open" & one "weld" costs $3.
a ring...
$3× 5 pairs = $15
Move on! 11
Global Math Challenge | Sample
03 Explanation Step ② Can we make fewer than five pairs? a e What if there were fewer joints?
b
Reduce the number of joint rings! c
d
Choose "Ring Set [c] and cut all the rings open! Then use those rings as joints between the rest of ring sets [a, b, d & e].
a
1 2
e open
weld
b
3 4 d Now, we only need 4 pairs of "open" & "weld"! meaning...the lowest cost possible is
Therefore, the answer is ”12”.
12
$3×4 pairs = $12
Global Math Challenge | Sample
04 Juice Bottles Question
Juice fills the bottle up to the red arrow, 9 cm from the bottom. When you turn the bottle upside down, the juice comes to 3 cm above the arrow as Fig 1.
Next, you take a glassful of juice from the bottle and then turn the bottle upside down. In this case, it fills up to the red arrow as Fig 2.
How many glasses of juice does this bottle hold?
Answer
The answer is 5 glasses. Go to the explanation!
13
Global Math Challenge | Sample
04 Explanation a -1
a -2
b 9 cm
9 cm 3 cm
9 cm
before taking a glassful
after taking a glassful
Step ① How much is in a glass of juice? a -2
b 9 cm
9 cm 3 cm
3 cm
3 cm for one glass 3 cm
amount of one glass
before
after
Step ② How much juice/space was there in the bottle to start?
a -1
a -2 3 cm 9 cm
amount of 3 glasses
3 cm 3 cm
You can add 2 more glasses!
3 cm
9 cm
amount of 3 glasses
3 cm 3 cm
before
before same amount
Move on! 14
Global Math Challenge | Sample
04 Explanation Result As in step ②, when you pour juice in the bottle [a-2] to fill it up...
a -2 3 cm 9 cm
9 cm
3 cm
3 glasses
3 glasses
The bottle contains 5 glasses of juice.
Therefore, the answer is:
2 glasses
5 glasses
15
Global Math Challenge | Sample
05 Apples & Oranges Question
We have 18 apples and oranges altogether, and there are more oranges than apples. Now we divide them into two groups of nine and put them on plates. Both plates have at least one apple and one orange. When one plate has seven apples on it, how many oranges do we have in total?
1
8
2
9
3
10
4
11
5
12
Answer
The answer is
3 10.
Go to the explanation!
16
Global Math Challenge | Sample
05 Explanation Read the question carefully, and solve the problem step by step.
Question Let's stop here for now.
We have 18 apples and oranges altogether, and there are more oranges than apples.
Now we divide them into two groups of nine and put them on plates. Both plates have at least one apple and one orange. When one plate has seven apples on it, how many oranges do we have in total?
Line all the apples and oranges up in a row.
Step①
１８ half (9) 1
2
3
4
5
half (9) 6
7
8
There are 8 apples at most.
There are more oranges...
There are fewer apples...
There are apples up to 8 !!
Move on!
17
Global Math Challenge | Sample
05 Explanation Question
We have 18 apples and oranges altogether, and there are more oranges than apples. Now we divide them into two groups of nine and put them on plates. Both plates have at least one apple and one orange. When one plate has seven apples on it, how many oranges do we have in total?
Step②
9
9
There are 7 apples out of 9.
There is at least one apple and one orange.
There are 2 oranges.
There are already 8 apples in total.
Result
So, there are ８ apples, and the rest are all oranges! Therefore, the answer is ”
10 ”. 18
