Download Solutions 1. My brother gave me two coins and I gave away one. My

Math in Action 2013-2014
Solutions
1.
My brother gave me two coins and I gave away one. My mom gave me 3 coins and I
gave away one. My dad gave me 4 coins and I gave away one. If I started with 5 coins,
how many coins do I have now?
Answer:
11
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1+2+3+5 = 11
2.
3.
There are three baskets, a brown one, a red one and a pink one, holding a total of ten
eggs.
The Brown basket has one more egg in it than the Red basket.
The Red basket has three eggs less than the Pink basket.
How many eggs are in each basket?
Trish had nine cards, each with a different number from 1 to 9 on it. He put the cards
into three piles so that the total in each pile was 15. Find 4 different ways Trish could
have done this.
Answer:
Brown basket: 3
Red basket: 2
Pink: 5
_____________
Answer:
Possible ways:
Pile 1
Pile 2
These are a few possible ways:
Pile 1
2, 3, 9, 1
3, 8, 4
5, 2, 8
6, 1, 8
9, 6
1, 2, 3, 4, 5
9, 1,5
9, 6
4.
Pile 2
6, 5, 4
6, 7, 2
1, 3, 4, 7
5, 7, 3
8, 4, 3
9, 6
7, 8
3, 5, 7
Pile 3
7, 8
9, 1, 5
9, 6
2, 4, 9
7, 5, 2, 1
7, 8
4, 3, 6, 2
1, 8, 2, 4
Mrs. Thompson was making three traditional English plum puddings.
She had ten old golden coins and wanted to put at least two in each pudding.
How many ways could the ten coins be placed into
three puddings so that each pudding ended up
with at least two coins?
______________
Answer:
4
______________
We know that each pudding must have at least two coins.
No pudding can have more than six coins, or there wouldn't be enough left for the other two.
If one pudding has six coins, then the other two must each have two coins, and that uses all ten.
If one pudding has five coins, then one of the others must have three and the other two.
If one pudding has four coins, then either another could have four and the third just two, or the remaining
two could have three each.
If no pudding has four or more coins, then we wouldn't have used all the coins. So these four possibilities
are the only ones.
5.
When Jack was one year old his mother bought a packet of 24 candles for his birthday
cake. That year she put 1 candle on Jack's cake. When he was two he had 2 candles and
when he was three he had 3 candles, and so on.
Answer:
Jack was 3
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One day Jack's little sister Kate was born. She had 1 candle on her first birthday cake,
2 candles on her second birthday cake, and so on. The candles were finished on one of
Jack's birthdays with just enough left. How old was Jack when Kate was born?
6.
Susie had a large bowl of cherries. They were all in pairs.
Susie took out a pair, she ate one cher5ry and put the other one back. She took out
another pair and did the same again.
Then she helped herself to one of the single cherries in the bowl.
Answer:
56
_______________
Pile 3
Math in Action 2013-2014
Susie continued helping herself to the cherries in this way (pair, pair, single - pair, pair,
single - ...)
After she had done this lots of times, there were just 14 single cherries left.
How many cherries had there been in the bowl to start with?
Table of results for
Cherries Come in
Two's!
Start
End
4
1
8
2
12
3
16
4
20
5
24
6
28
7
32
8
36
9
40
10
44
11
48
12
52
13
56
14
7.
A certain number has exactly eight factors including 1 and itself. Two of its factors are 21
and 35. What is the number?
If 21 and 35 are factors of the number, then 3, 5 and 7 must all be included amongst its prime factors. This means that the
required number must be a multiple of 105 and, as the complete list of factors of 105 is 1, 3, 5, 7, 15, 21, 35 and 105, the
answer is 105.
8.
If you write plus signs between each of the digits 1 to 9, this is what you get:
1+2+3+4+5+6+7+8+9=45
However, if you alter where the plus signs go, you could also get:
12+3+45+6+7+8+9=90
Can you put plus signs in so this is true?
1 2 3 4 5 6 7 8 9 = 99
Answer:
105
_______________
Answer:
Possible solutions:
1+23+45+6+7+8+9=99
12+3+4+56+7+8+9=99
1+2+3+4+5+67+8+9=99
________________________
Find at least one solution.
9.
In sheep talk the only letters used are B and A. Sequences of words
are formed as follows:
The first word only contains the single letter A.
To get the next word in the sequence change each A in the previous word into B and
each B in the previous word into AB. The first 4 sequences are given below.
Answer:
Use the blank space
below the problem
Write down the first ten words in this sequence.
Count the number of A's in each word in the sequence. Then count the number of B's in
each word in the sequence. Finally count the number of letters in each word in the
sequence. You now have three sequences of numbers. What do you notice? Will the
same patterns continue if you generate longer sequences of words?
A
B
AB
BAB
ABBAB
BABABBAB
ABBABBABABBAB
BABABBABABBABBABABBAB
ABBABBABABBABBABABBABABBABBABABBAB
BABABBABABBABBABABBABABBABBABABBABBABABBABABBABBABABBAB
Notice that all the totals are Fibonacci numbers and the A column is what the B column was last row, and
the B column is what the total used to be in the last row. Therefore the next numbers will be:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
A
B
Total
1
0
1
1
2
3
5
8
13
21
0
1
1
2
3
5
8
13
21
34
1
1
2
3
5
8
13
21
34
55
Math in Action 2013-2014
_______________
This is because the A's come from the B's in the previous row and the B's come from the A's and B's (the
total) in the previous row.
10. To paint all sides of a cube that was built out of
little cubes (see Figure 2) 9 gallons of paint was
used. How many gallons of paint are needed to
paint the white region of the solid shown in
Figure 1?
To paint all six sides of the figure we need 9 gallons of paint.
To paint one side of the figure (with 9 faces of cubes), we need
9/6 = 3/2 gallon of paint.
To paint 1 face of a cube: we need 3/2÷9 = 3/2 x 1/9 = 3/18 or 1/6
gallon of paint.
Since the white region has 12 faces to paint, we need: 12 x 1/6 = 2 gallon of paint.
Answer:
2
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