Line all the apples and oranges up in a row. Move on! Stepâ . 1. 2. 3. 4. 5. 6. 7. 8. 18. We have 18 apples and oranges altogether, and there are mor...

4 downloads 95 Views 907KB Size

No documents

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