Much of mathematics is looking for and applying useful patterns. For instance, what is the sum of the first 320 odd numbers? By looking at the pattern for the sum of the 1st two odd numbers (1+3=4), the 1st three odd numbers (1+3+5=9), the 1st four odd numbers ( 1+3+5+7=16) and so on, the sum of the first 320 odd numbers is quickly solved. (320 ²)

Other problems are listed below.

Here are the other problem solving strategies:

• Guess and Check
• Make A Systematic List
• Make A Drawing Or Model
• Simplify the Problem

  Look for a Pattern Problems

  

  Day 6 - What is the sum of the first 4 odd numbers? 5 odd numbers? 7 odd numbers? 10 odd numbers? 2356 odd numbers?

  

  Day 7 - Find the pattern. Fill in the blanks. (a) 1 , 4 , 9 , 16, 25, __, __, __ (b) 3, 4, 7, 11, 18, 29, __, __, __ (c) 5, 10, 9, 18, 17, 34, 33, __, __ (d) 1, 2, 6, 24, 120, __, __, __ (e) 77, 49, 36, 18, __

  

  Day 8 - Find these products: 7 x 9, 77 x 99, 777 x 999, Predict the product for 77,777 x 99999. What two numbers give a product of 77,762,223?

  

  Day 9 - For each problem, give the missing numbers or expression: (a)

  1	2	3	4	5	8	10	?
  3	6	9	12	?	?	?	48

  (b)

  1	2	3	4	5	9	12	?
  3	5	7	9	?	?	?	37

  (c)

  1	2	3	4	5	8	?
  1/2	1/6	1/12	1/20	?	?	1/11

  

  Day 10 -

  Power of 2	21	22	23	24	25	26	27	28
  Units digit	2	4	?	?	?	?	?	6

  Predict the units digit for these:

  212

  236

  29

  225

  239

  242

  

  Day 31 - Determine the number of integers between 1 and 1000 that contain at least one 2 but no 3.

  

  Day 32 - How many numbers less than 124 are divisible by 2, 3 and 5?

  

  Day 33 - Can you find a number that fits this pattern? 3600 , 1800, 600, 150, __?__

  

  Day 34 - If you added 6 rows to the bottom of this picture, how many small triangles would you have altogether?
  

  

  Day 35 - 1990 - 1980 + 1970 - 1960 + ..... - 20 + 10 = ?

  

  Day 56 - Find the following sum: 1/(1x2) +1/(2x3) + 1/(3x4) + ..... + 1/(99x100)

  

  Day 57 - What is the units digit of this sum? 1! + 2! + 3! + ...... + 14! + 15!

  

  Day 58 - How many squares are contained in a 5 x 5 square grid?

  

  Day 59 - Express as a single fraction is lowest terms: 1/(1x2) + 1/(2x3) + 1/(3x4) + ..... + 1/(9x10)

  

  Day 60 - Find a possible next number for this sequence: 3 , 7, 16, 32, 57. 93, ___

  

  Day 81 - What is the ones digit of 3¹⁹⁹²?

  

  Day 82 - A town has a population of 300,000 with an annuall growth rate of 4.5%. At that rate, in how many years will the population be 500,000?

  

  Day 83 - What is a + b ?

  

  Day 84 - What is the sum of the prime factors of the number represented by: 2¹² - 2¹¹ +2¹⁰ - 2⁹ + ...... +2² - 2¹?

  

  Day 85 -

  
  What will row 50 look like? Can you generalize the result for any row of the triangle?

  

  Day 106 - Fill in the missing terms of this pattern: 102, 105, 111, 114, 120, 123, 129, ____, ____, ____, ____, ____, 201, 204, 210, 213, 219, .....

  

  Day 107 - The positive integers are written in a triangular array as shown. In what row is the number 1000?
  1
  2 3
  4 5 6
  7 8 9 10 ...

  

  Day 108 - What is the sum of the numbers in the 100th row of the triangular array in problem 107?

  

  Day 109 - If this pattern continues, what is a possible next number in the sequence 1, 7, 25, 61, 121, ...?

  

  Day 110 - The positive numbers are written in the pattern shown. Find the number in the 100th row and 100th column
  .

  

  Day 131 - Fill in the blank with a number to complete the following pattern: ____, 1661, 1771, 1881, 1991, 2002, ...

  

  Day 132 - If this lattice were continued, what number would be directly to the right of 98?

  

  

  Day 133 - What could the next four numbers in this progression be? 12, 1, 1, 1, 2, 1, 3, ___, ___, ___, ___

  

  Day 134 - In what row and c olumn is 1996?
  

  

  Day 135 - How many terms are in the following sequence? 10, 17, 24, 31, ..., 374