Christmas Maths Challenge

Here is a problem which might require a little perseverance.  There is more than one solution.

Make a Century

By putting arithmetical signs (+ , - , x ) in suitable places between the digits make the following sum correct:

1   2   3   4   5   6   7   8   9  =  100

Note: The digits must remain in counting order but the spaces may be removed to make two or three digit numbers.  For example, the space between the 2 and 3 can be eliminated to make 23.  Brackets may be used if necessary.

Bring your solution(s) to Mrs. Hopkins by Thursday January 8th. The person who can find the most solutions will be able to have an extra session helping in Nursery (during lesson time).

Rudolph's Nose Solution

1. He will need 9 light bulbs.  (There are 3 sets of 8 hours in 24 hours.  Rudolph needs 3 new bulbs for each set of 8 hours. 3 x 3 = 9)

2. Santa will need to spend £11.25.  (9 x 1.25 = 11.25)

Rudolph's Nose **

1. Rudolph the red-nosed reindeer has 3 red light bulbs in his nose and they blow out every 8 hours.  How many light bulbs will Rudolph need if his nose is going to glow for 24 hours?

2. If Rudolph's bulbs cost £1.25 each, how much will Santa need to spend for 24 hours worth of bulbs?

Santa Buys Name Tags Solutions

a) Rudolph, Prancer and Blitzen have the most expensive names.

b) Comet, Vixen and Cupid have the least expensive names.

(Did anyone notice that all the names have 2 vowels so you only need to look at the number of consonants to discover who had the most or least expensive names?)

c) Dasher = £29.40
Prancer = £35.10
Comet = £23.70
Donner = £29.40
Rudolph = £35.10
Dancer = £29.40
Vixen = £23.70
Cupid = £23.70
Blitzen = £35.10

Santa Buys Name Tags *

Santa decides to buy name tags for his reindeer.  The names are:
Dasher, Dancer, Prancer, Vixen. Comet, Cupid, Donner, Blitzen and Rudolph.

For each name tag, vowels cost £3.30 and consonants cost £5.70.

a) Which 3 reindeer are tied for the most expensive names?
b) Which 3 reindeer are tied for the least expensive names?
c) How much did Santa pay for the name tags for all 9 reindeer?

Variation - Change the cost of the letters to make the challenge easier or more difficult.  For example, younger children may be able to add together whole pounds (ie. vowels = £3 and consonants £5) instead of working with pounds and pence together.

Make 24! Solutions

A) 3 x 4 + 7 + 5

B) 11 + 10 + (6 ÷ 2)

C) 6 x 8 ÷ 2 x 1

D) 8 x [7 – (3+1)]

E) 5 x 6 – 4 - 2

Make 24! *****

Use all of the numbers and any of the four operations (+, -, x, ÷) to make number sentences that equal 24.

Example: 6  2  3  8           Solution: 6 x 3 + 8 -2

A)  5  4  7  3 

B)  11   10   2   6

C)  1   2   6   8

D)  1   3   7   8

E)  2   4   5   6

Helpful hint:  Think about the order of operations BIDMAS.  You can use an operation more than once in each solution.  If you get stuck on one move onto another one and then go back. 

Subtraction Snap *

Purpose:

To practise subtraction and immediate recall of facts.

Players: 2

Equipment:    - deck of cards: Ace to 9 (Ace =1)

Instructions:

• Players divide the cards evenly between themselves.
• Each player turns over one card at the same time. Players must subtract the smaller number from the larger number of the two cards and say their answer out loud.  The first player to say the correct answer collects both cards.
• In the event of a tie, set both cards aside and continue play.  The winner of the next round that doesn’t end in a tie takes all the cards set aside by ties.
• Play continues for a set amount of time or one player loses all their cards.  The player with the most cards is the winner

Variation:

For a three-player game, assign two players as the addition cards.  (Add their card values together.)  The third player’s card will be subtracted from the sum of the other two.

What is the missing number? Solution

Solution:

7	3	4
12	5	7
9	2	7

The missing number is 7.  In each row, the first number minus the second equals the third.

8	5	40
9	2	18
6	4	24

The missing number is 4.  In each row, the first number times the second number equals the third number.

What is the missing number? **

Each puzzle has a missing number.  
Can you work out what it is?  
Try to justify your answer.
 

7	3	4
12	5	7
9	2	?

 

8	5	40
9	2	18
6	?	24

 
Make up your own missing number problems.

10 Pence Solution

There are eleven differrent ways to give somebody 10 pence.

10

5, 5

5, 2, 2, 1

5, 2, 1, 1, 1

5, 1, 1, 1, 1, 1

2, 2, 2, 2, 2

2, 2, 2, 2, 1, 1

2, 2, 2, 1, 1, 1, 1

2, 2, 1, 1, 1, 1, 1, 1

2, 1, 1, 1, 1, 1, 1, 1, 1

1, 1, 1, 1, 1, 1, 1, 1, 1, 1

10 Pence **

How many different ways are there to give someone 10 pence?

Helpful Tips:  Work in an organized way.  Perhaps start with larger value coins and work your way down to the smaller value coins.  Use real coins to help you. 

Number Mazes Solution

13 = 1 + 2 + 2 + 1 + 7

38 = 4 + 9 + 9 + 8 + 8

34 = 10 + 6 + 1 + 2 + 10 + 5

Number Mazes ***

Start in the yellow square and move to the orange square by adding up the numbers along the way.  You need the correct total before reaching the end.  The orange square shows you what total you need to make.  You are only allowed to visit each square once and you can only move vertically and horizontally.

	1	2	5
	2	7	7
	2	1	7	13

	4	9	6
	1	9	8
	7	4	8	38

	10	6	5
	5	1	0
	3	2	6
	7	10	5	34

Who is in the middle? Solution

Isobel is in the middle.

Taking the sentences in order:

Sarah is shorter than Isobel.

Sarah is shorter than Emily, who is shorter than Isobel. 

Finally Sarah is shorter than Emily, who is shorter than Isobel, who is shorter then Alice, who is shorter than Rachel.

Who is in the middle? ****

Isobel is taller than Sarah.  Emily is shorter than Isobel, but taller than Sarah.  Alice is shorter than Rachel, but taller than both Emily and Isobel.  Whose height is the middle for the group?