Added missing problem statements

project_euler/README.md

@@ -37,21 +37,77 @@ PROBLEMS:
 
 7. By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.
    What is the Nth prime number?
+
+8. Find the consecutive k digits in a number N that have the largest product.
 
 9. A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
     a^2 + b^2 = c^2
     There exists exactly one Pythagorean triplet for which a + b + c = 1000.
     Find the product abc.
 
+10. Find sum of all prime numbers below 2 million.
+
+11. In the given 20x20 grid, find 4 adjacent numbers (horizontally, vertically or diagonally) that have the largest product.
+
+12. The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:
+
+    1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
+
+    Let us list the factors of the first seven triangle numbers:
+
+    1: 1
+    3: 1,3
+    6: 1,2,3,6
+    10: 1,2,5,10
+    15: 1,3,5,15
+    21: 1,3,7,21
+    28: 1,2,4,7,14,28
+    We can see that 28 is the first triangle number to have over five divisors.
+
+    What is the value of the first triangle number to have over five hundred divisors?
+
+13. Work out the first 10 digits of the sum of the given hundred 50 digit numbers.  
+
 14. The following iterative sequence is defined for the set of positive integers:
     n → n/2 (n is even)
     n → 3n + 1 (n is odd)
     Using the rule above and starting with 13, we generate the following sequence:
     13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
     Which starting number, under one million, produces the longest chain?
+
+15. Starting from top left corner of a 20x20 grid how many routes are there to reach the bottom left corner?
 
 16. 2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.
     What is the sum of the digits of the number 2^1000?
+
+17. If the numbers 1 through 1000 were written in words, how many total letters would be used?
+
+18. By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.
+   3
+  7 4
+ 2 4 6
+8 5 9 3
+
+That is, 3 + 7 + 4 + 9 = 23.
+
+Find the maximum total from top to bottom of the triangle below:
+
+              75
+             95 64
+            17 47 82
+           18 35 87 10
+          20 04 82 47 65
+         19 01 23 75 03 34
+        88 02 77 73 07 63 67
+       99 65 04 28 06 16 70 92
+      41 41 26 56 83 40 80 70 33
+     41 48 72 33 47 32 37 16 94 29
+    53 71 44 65 25 43 91 52 97 51 14
+   70 11 33 28 77 73 17 78 39 68 17 57
+  91 71 52 38 17 14 91 43 58 50 27 29 48
+ 63 66 04 68 89 53 67 30 73 16 69 87 40 31
+04 62 98 27 23 09 70 98 73 93 38 53 60 04 23
+
 20. n! means n × (n − 1) × ... × 3 × 2 × 1
     For example, 10! = 10 × 9 × ... × 3 × 2 × 1 = 3628800,
     and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27.