# Number Patterns Challenge

After browsing through some puzzles on here, I found some that have letter patterns, such as P, N, D, ? for Penny, Nickel, Dime, and ... (you know what comes next). Now, I've decided to do some number patterns instead. Some patterns may be based off of something else, such as coin values and dates.

Some amount of math may be required for these.

Warm-Up (find the next 1)

1. 1, 4, 9, 16, ?

2. 17, 19, 23, 29, 31, ?

Easy (find the next 1)

1. 1, 2, 5, 10, 20, 50, ?

2. 31, 28, 31, 30, 31, ?

3. 01, 02, 06, 24, 20, 20, ?

Medium (find the next 2)

1. 20, 90, 61, 32, 03, ?, ?

Hint given after 7 days if no solution; the hint kind of gives it away.

2. 1, 8, 28, 56, 70, ?, ?

Hint given after 7 days if no solution; the hint kind of gives it away.

3. 8, 4, 2, 6, 2, 8, 6, 4, 4, ?, ?

Alternating pattern

4. 1, 7, 15, 3, 4, 11, 9, ?, ?

Modular arithmetic

Hard (find the next 2)

1. 111, 112, 115, 120, 122, 124, 126, 128, 132, 135, ?, ?

Divisibility with digits

2. 1, 4, 31, 224, 2011, ?, ?

Multiplying in something other than base 10.

Make a comment if one of the patterns is in the wrong difficulty.

It might be helpful to add your answers as you find them instead of adding one big bunch in the end; to receive best answer you must have 1-9 solved and posted as a solution; 10 and 11 will have a bounty if not solved by 10 days.

• Generally, number sequences with no hints are not well-received, since they can be viewed as being fairly arbitrary. I would suggest adding a starting point for some of the harder sequences! – Bailey M Jul 29 '15 at 21:01
• Is there a mistake with number 5? – mmking Jul 29 '15 at 21:20
• @mmking, It might not be the pattern you're thinking of, but no, there's not a mistake. – Vincent Tang Jul 29 '15 at 21:21

Still working on some, but here's what I have:

Warm-Up (find the next 1)

1. 1, 4, 9, 16, ?

25 (list of squares of integers starting with 1)

2. 17, 19, 23, 29, 31, ?

37 (list of primes starting with 17)

Easy (find the next 1)

1. 1, 2, 5, 10, 20, 50, ?

100 (list of US dollar denominations)

2. 31, 28, 31, 30, 31, ?

30 (list of lengths of months in days starting with January)

3. 01, 02, 06, 24, 20, 20 ?

Medium (find the next 2)

1. 20, 90, 61, 32, 03, ?, ?
2. 1, 8, 28, 56, 70, ?, ?

56, 28 (list of numbers in 9th row of Pascal's Triangle)

3. 8, 4, 2, 6, 2, 8, 6, 4, 4, ?, ?

4. 1, 7, 15, 3, 4, 11, 9, ?, ?

12,16 (7^n mod 17)

Hard (find the next 2)

1. 111, 112, 115, 120, 122, 124, 126, 128, 132, 135, ?, ?

140, 144 (list of integers that are divisible by each of their digits starting with 111)

2. 1, 4, 31, 224, 2011, ?, ?

13044, 112341 (convert from base 5 to base 10, multiply by 4, convert back to base 5)

• Looking good so far. – Vincent Tang Jul 29 '15 at 21:18
• #6 is 73 and 44, because it's subtraction by 29 modulo 99. – Joe Z. Jul 30 '15 at 1:26
• #5 maybe its 40, pattern would be n = (n-1)([position of n-1]+1) mod 100 – The random guy Jul 30 '15 at 6:52
• #5 is not 40; #6 is 73 and 4; just #8 left – Vincent Tang Jul 30 '15 at 19:45

I'll answer some of the ones that haven't been answered so far:

5. 40, 20 (last two digits in factorials)

6. 73, 44 (subtract 29 modulo 99 each time)

1.

25 (+3 +5 +7 +9)

2.

35 (+2 +4 +6 +2 +4)

• #1 is right, #2 is not right. (Remember, some, but probably only a little, math may be involved.) – Vincent Tang Jul 29 '15 at 21:17