First Name: ____________________
Last Name:___________________________
Teacher: _______________ Parent’s email:
Grade: ____
_________________________________________
Numbers and Digits
Welcome to Math Challenge #1. In this first challenge, try to discover the missing digit(s) or number(s). Get
familiarized with the different strategies of problem solving www.mathinaction.org. Ask your sibling or an adult
for help if you get stuck.
Numbers vs Digits
The difference between a digit and a number is similar to the difference between a letter or a character and a
word. Just like alphabetical letters make words, digits make numerals, which is a representation of a number.
· Numbers are made up of digits, and digits make numbers.
· A digit is a symbol, and number may consist of one or more digits.
· A number has a numerical value, while digit is just a representation.
Kinder & First Grade: solve at least 3 problems.
Second & Third Grade: solve at least 7 problems.
Fourth Grade and above: solve at least 12 problems.
Problems
1.
What is the number that is covered by the flower?
9 +
Answer:
6
= 15
2.
If you arrange the following numbers from least to greatest, which would be the 4th
number?
13 21 14 31 32 23
23
3.
Look at the pattern below. What are the missing numbers?
17 and 22
2, 7, 12, ____, ____, 27, 32, 37
4.
What is the missing digit?
5.
If you add 211 and 221, which digit will be in the tens place?
6.
What number represents the value of
×
×
5
3 ?
+ 9
4 4
+
3
9 + 7 = 16
?
= 81
= 49
7.
Joy wrote a one-digit number then wrote an additional digit to its right. She subtracted 5
from this number and got 29. What was the number Joy wrote first?
3
8.
What is the number that is covered by the star?
9
9.
The number on Mr. Sarwono’s motorcycle license plate has three digits. The product of the
digits is 216. The sum of the three digits is 19. What is the greatest three-digit number that
could be on his license plate?
6×
= 13 + 41
964
List all numbers whose digit-sum is 19 (991, 982, 973,…, 775, 766) and find whose product is 216.
2016-2017 Math Challenge
10.
Behind these four cards is a four-digit number. Each card contains a digit. The digit in the
ones place is the largest possible single digit number. The digit in the hundreds place is the
smallest odd number. The digit in the tens place is 1 less than
the digit in the ones place. The digit in the thousands place is
the sum of the digits in the hundreds and tens places. Find
this four digit number.
9189
Ones place: Largest possible single digit number is 9. Hundreds place: smallest odd number is 1. Tens place: 9-1 = 8.
Thousands place: 8+1=9. The four-digit number is 9189.
11.
George wrote three numbers on three different cards. The sum of the three numbers is
3500. The first number is 525 more than the second number. The second number is 158
less than the third number. What are the three numbers?
First number:
Second number:
Third number:
12.
+525
3500
+158
1464, 939,
and 1097
3 equal parts = 3500 – 525 – 158 = 2817
1 part = 2817 ÷ 3 = 939
First number: 939+525 = 1464
Second number: 939; third number: 939 + 158 = 1097
Angela is trying to remember a three-digit number lock for her suitcase. She
knows that it is between 100 and 115. When she divides the three-digit number
by 6, it gives her a remainder of 4. When she divides the three-digit number by 3,
she gets a remainder of 1. Help Angela remember the three-digit number.
Two numbers
for Angela to
try:
106 and 112
Numbers that are divisible by 6, between 100 and 115, with a remainder of 4: 106 and 112.
Numbers that are divisible by 3, between 100 and 115 with a remainder of 1: 103, 106, 109, and 112. Answer:
106 or 112. Angela should try these two numbers.
13.
Study this pattern:
4+5+6+7+8 = 30
5+6+7+8+9 = 35
6+7+8+9+10 = 40
Fill in the missing numbers based on the pattern above.
____+____+____+____+____= 65
14.
If you continue the pattern, you will get:
7+8+9+10+11 = 45
8+9+…+12 = 50
9+10+…+13= 55
10+11+…+14 = 60
11+12+…+15 = 65
Using the following clues, find the two 2-digit numbers covered by the hands.
- When you divide each number by 5, there will be a remainder of 3.
- When you divide each number by 8, there will be a reminder of 3.
11, 12, 13, 14,
and 15
43 and 83
Adding 3 to multiple of 5: 8, 13, 18, 23, 28, 33, 38, 43, 48, …, 73, 78, 83, 88, …, 93, 98.
Adding 3 to multiple of 8: 11, 19, 27, 35, 43, 51, …, 75, 83, 91, 99. The two possible numbers are 43 and 83.
15.
Complete the addition using different digits for different letters. A = 7, D = 5, M = 9, T = 4.
Find the value of “SHARP”.
ADD
IT
UP
MATH
+
I S
SHARP
16.
Y
17.
10723
First write the problem with the known digits. S should be equal to
1 as we cannot get 5-digit number from adding 4-digit number and
smaller ones. Then H = 0. To get hundreds place digit 7 we should
have carryover of 3 from adding D + I + U + T + I, thus I = 8. Doing
these steps will lead you to the answer: SHARP = 10723
Using the clues below, what number is Y?
- Y is a two digit-prime
- Y + 3 is a perfect square
- Y + 6 is the next greater two-digit prime
61
There are fewer 2-digit perfect squares than 2 digit primes, so start
with the squares: Y+3 -> 16, 25, 36, 49, 64, 81. Check if Y is prime or
not, when you subtract it by 3. Then check if Y+6=prime. If you list
things correctly, you will find that Y = 61.
Sylvia, who was born in 2008, asked Mr. Harris, “How old were you in the year I was
born?” “My age was the sum of all the digits of my year of birth,” replied Mr. Harris. How
old was he in 2008? He was born in 19AB. 2008 – 1900 – 10A – B = 10+A+B  Simplify: 11A = 98 – 2B  A
23
= (98 -2B)/11. So when B =5, A = 88/11=8. 2008 – 1985 = 23; Check: 1+9+8+5 = 23. Mr. Harris was 23 years old.
2016-2017 Math Challenge