-
Notifications
You must be signed in to change notification settings - Fork 0
/
ProjEuler.lhs
650 lines (561 loc) · 31.9 KB
/
ProjEuler.lhs
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
My solutions for Project Euler[1] in literate Haskell.
[1] http://projecteuler.net/
======================================================================
> import Data.Char
> import Data.List
Some simple mathematics.
======================================================================
> primes = let diff xs@(x:xt) ys@(y:yt) = case compare x y of
> LT -> x : (diff xt ys)
> EQ -> diff xt yt
> GT -> diff xs yt
> merge xs@(x:xt) ys@(y:yt) = case compare x y of
> LT -> x : (merge xt ys)
> EQ -> x : (merge xt yt)
> GT -> y : (merge xs yt)
> f (x:xt) ys = x : (merge xt ys)
> g p = [ n * p | n <- [p, p + 2 ..]]
> nonprimes = foldr1 f . map g . tail $ primes
> in [2, 3, 5] ++ (diff [7, 9 ..] nonprimes)
> fibonacci = 1:2:(zipWith (+) fibonacci $ tail fibonacci)
> primeFactors n = let g n x k | n `rem` x == 0 = g (n `quot` x) x (k + 1)
> | otherwise = (n, k)
> f (x:xt) n = if n == 1
> then []
> else let (l, k) = g n x 0
> in if k == 0
> then f xt n
> else (x, k) : f xt l
> in f primes n
Problem starts here.
======================================================================
Problem 1
05 October 2001
If we list all the natural numbers below 10 that are multiples of 3 or
5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below 1000.
> p1 = sum $ filter (\x -> x `rem` 3 == 0 || x `rem` 5 == 0) [1..999]
Problem 2
19 October 2001
Each new term in the Fibonacci sequence is generated by adding the
previous two terms. By starting with 1 and 2, the first 10 terms will
be:
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
Find the sum of all the even-valued terms in the sequence which do not
exceed four million.
> p2 = sum $ filter even $ takeWhile (<= 4000000) fibonacci
Problem 3
02 November 2001
The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the number 600851475143 ?
> p3 = let f xs@(x:xt) p n
> | n < x = p
> | n `rem` x /= 0 = f xt p n
> | n `rem` x == 0 = f xs x $ n `quot` x
> in f primes 1 600851475143
> p3' = let f x n | n < x*x = n
> | n `rem` x /= 0 = f (x + 1) n
> | n `rem` x == 0 = f (x + 1) (n `quot` x)
> in f 2 600851475143
Problem 4
16 November 2001
A palindromic number reads the same both ways. The largest palindrome
made from the product of two 2-digit numbers is 9009 = 91 × 99.
Find the largest palindrome made from the product of two 3-digit
numbers.
> p4 = let ddd = [999,998..100]
> num = [x * y | x <- ddd, y <- ddd, x <= y]
> palindrome n = let s = show n
> in s == reverse s
> in head . filter palindrome $ sortBy (flip compare) num
Problem 5
30 November 2001
2520 is the smallest number that can be divided by each of the numbers
from 1 to 10 without any remainder.
What is the smallest number that is evenly divisible by all of the
numbers from 1 to 20?
> p5 = foldr lcm 1 [2..20]
Problem 6
14 December 2001
The sum of the squares of the first ten natural numbers is,
1^(2) + 2^(2) + ... + 10^(2) = 385
The square of the sum of the first ten natural numbers is,
(1 + 2 + ... + 10)^(2) = 55^(2) = 3025
Hence the difference between the sum of the squares of the first ten
natural numbers and the square of the sum is 3025 − 385 = 2640.
Find the difference between the sum of the squares of the first one
hundred natural numbers and the square of the sum.
> p6 = let ns = [1..100]
> in sum [ x * y | x <- ns, y <- ns, x /= y]
Problem 7
28 December 2001
By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can
see that the 6^(th) prime is 13.
What is the 10001^(st) prime number?
> p7 = primes !! 10000
Problem 8
11 January 2002
Find the greatest product of five consecutive digits in the 1000-digit
number.
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
> p8 = let str = "73167176531330624919225119674426574742355349194934\
> \96983520312774506326239578318016984801869478851843\
> \85861560789112949495459501737958331952853208805511\
> \12540698747158523863050715693290963295227443043557\
> \66896648950445244523161731856403098711121722383113\
> \62229893423380308135336276614282806444486645238749\
> \30358907296290491560440772390713810515859307960866\
> \70172427121883998797908792274921901699720888093776\
> \65727333001053367881220235421809751254540594752243\
> \52584907711670556013604839586446706324415722155397\
> \53697817977846174064955149290862569321978468622482\
> \83972241375657056057490261407972968652414535100474\
> \82166370484403199890008895243450658541227588666881\
> \16427171479924442928230863465674813919123162824586\
> \17866458359124566529476545682848912883142607690042\
> \24219022671055626321111109370544217506941658960408\
> \07198403850962455444362981230987879927244284909188\
> \84580156166097919133875499200524063689912560717606\
> \05886116467109405077541002256983155200055935729725\
> \71636269561882670428252483600823257530420752963450"
> f [] = []
> f ds = product (take 5 ds) : f (tail ds)
> in maximum . f $ map digitToInt str
Problem 9
25 January 2002
A Pythagorean triplet is a set of three natural numbers, a < b < c,
for which, a^(2) + b^(2) = c^(2)
For example, 3^(2) + 4^(2) = 9 + 16 = 25 = 5^(2).
There exists exactly one Pythagorean triplet for which a + b + c =
1000.
Find the product abc.
> p9 = let ds = [1..500]
> l = [a * b * (1000- a - b) | a <- ds, b <- ds,
> a < b, a^2 + b^2 == (1000 - a - b)^2]
> in head l
Problem 10
08 February 2002
The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
Find the sum of all the primes below two million.
> p10 = sum $ takeWhile (< 2000000) primes
Problem 11
22 February 2002
In the 20×20 grid below, four numbers along a diagonal line have been
marked in red.
08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
The product of these numbers is 26 × 63 × 78 × 14 = 1788696.
What is the greatest product of four adjacent numbers in any direction
(up, down, left, right, or diagonally) in the 20×20 grid?
> p11 = let gridStr = "08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08\n\
> \49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00\n\
> \81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65\n\
> \52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91\n\
> \22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80\n\
> \24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50\n\
> \32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70\n\
> \67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21\n\
> \24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72\n\
> \21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95\n\
> \78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92\n\
> \16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57\n\
> \86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58\n\
> \19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40\n\
> \04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66\n\
> \88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69\n\
> \04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36\n\
> \20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16\n\
> \20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54\n\
> \01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48"
> grid :: [[Int]]
> grid = map (map read . words) $ lines gridStr
> hFrom x y = zip (repeat x) [y..]
> vFrom x y = zip [x..] (repeat y)
> dFrom x y = zip [x..] [y..]
> dFrom' x y = zip [x..] [y, y-1..]
> nxy (x, y) = if x >= 0 && x < 20 && y >= 0 && y < 20
> then grid !! x !! y
> else 0
> indexList = [0..19]
> in maximum $
> map (product . take 4 . map nxy)
> [f x y |
> x <- indexList, y <- indexList,
> f <- [hFrom, vFrom, dFrom, dFrom']]
Problem 12
08 March 2002
The sequence of triangle numbers is generated by adding the natural
numbers. So the 7^(th) 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?
> p12 = let mergeFactors [] ys = ys
> mergeFactors xs [] = xs
> mergeFactors xs@((fx,nx):xt) ys@((fy,ny):yt)
> = case compare fx fy of
> LT -> (fx, nx) : mergeFactors xt ys
> EQ -> (fx, nx + ny) : mergeFactors xt yt
> GT -> (fy, ny) : mergeFactors xs yt
> reduce2 ((2, n):xs) = if n == 1
> then xs
> else (2, n - 1) : xs
> facs = map primeFactors [1..]
> ns = map (product . map ((+) 1 . snd) . reduce2) $
> zipWith mergeFactors facs (tail facs)
> num = fst . head . dropWhile ((< 500) . snd) $ zip [1..] ns
> in num * (num + 1) `quot` 2
Problem 13
22 March 2002
Work out the first ten digits of the sum of the following one-hundred
50-digit numbers.
37107287533902102798797998220837590246510135740250
46376937677490009712648124896970078050417018260538
74324986199524741059474233309513058123726617309629
91942213363574161572522430563301811072406154908250
23067588207539346171171980310421047513778063246676
89261670696623633820136378418383684178734361726757
28112879812849979408065481931592621691275889832738
44274228917432520321923589422876796487670272189318
47451445736001306439091167216856844588711603153276
70386486105843025439939619828917593665686757934951
62176457141856560629502157223196586755079324193331
64906352462741904929101432445813822663347944758178
92575867718337217661963751590579239728245598838407
58203565325359399008402633568948830189458628227828
80181199384826282014278194139940567587151170094390
35398664372827112653829987240784473053190104293586
86515506006295864861532075273371959191420517255829
71693888707715466499115593487603532921714970056938
54370070576826684624621495650076471787294438377604
53282654108756828443191190634694037855217779295145
36123272525000296071075082563815656710885258350721
45876576172410976447339110607218265236877223636045
17423706905851860660448207621209813287860733969412
81142660418086830619328460811191061556940512689692
51934325451728388641918047049293215058642563049483
62467221648435076201727918039944693004732956340691
15732444386908125794514089057706229429197107928209
55037687525678773091862540744969844508330393682126
18336384825330154686196124348767681297534375946515
80386287592878490201521685554828717201219257766954
78182833757993103614740356856449095527097864797581
16726320100436897842553539920931837441497806860984
48403098129077791799088218795327364475675590848030
87086987551392711854517078544161852424320693150332
59959406895756536782107074926966537676326235447210
69793950679652694742597709739166693763042633987085
41052684708299085211399427365734116182760315001271
65378607361501080857009149939512557028198746004375
35829035317434717326932123578154982629742552737307
94953759765105305946966067683156574377167401875275
88902802571733229619176668713819931811048770190271
25267680276078003013678680992525463401061632866526
36270218540497705585629946580636237993140746255962
24074486908231174977792365466257246923322810917141
91430288197103288597806669760892938638285025333403
34413065578016127815921815005561868836468420090470
23053081172816430487623791969842487255036638784583
11487696932154902810424020138335124462181441773470
63783299490636259666498587618221225225512486764533
67720186971698544312419572409913959008952310058822
95548255300263520781532296796249481641953868218774
76085327132285723110424803456124867697064507995236
37774242535411291684276865538926205024910326572967
23701913275725675285653248258265463092207058596522
29798860272258331913126375147341994889534765745501
18495701454879288984856827726077713721403798879715
38298203783031473527721580348144513491373226651381
34829543829199918180278916522431027392251122869539
40957953066405232632538044100059654939159879593635
29746152185502371307642255121183693803580388584903
41698116222072977186158236678424689157993532961922
62467957194401269043877107275048102390895523597457
23189706772547915061505504953922979530901129967519
86188088225875314529584099251203829009407770775672
11306739708304724483816533873502340845647058077308
82959174767140363198008187129011875491310547126581
97623331044818386269515456334926366572897563400500
42846280183517070527831839425882145521227251250327
55121603546981200581762165212827652751691296897789
32238195734329339946437501907836945765883352399886
75506164965184775180738168837861091527357929701337
62177842752192623401942399639168044983993173312731
32924185707147349566916674687634660915035914677504
99518671430235219628894890102423325116913619626622
73267460800591547471830798392868535206946944540724
76841822524674417161514036427982273348055556214818
97142617910342598647204516893989422179826088076852
87783646182799346313767754307809363333018982642090
10848802521674670883215120185883543223812876952786
71329612474782464538636993009049310363619763878039
62184073572399794223406235393808339651327408011116
66627891981488087797941876876144230030984490851411
60661826293682836764744779239180335110989069790714
85786944089552990653640447425576083659976645795096
66024396409905389607120198219976047599490197230297
64913982680032973156037120041377903785566085089252
16730939319872750275468906903707539413042652315011
94809377245048795150954100921645863754710598436791
78639167021187492431995700641917969777599028300699
15368713711936614952811305876380278410754449733078
40789923115535562561142322423255033685442488917353
44889911501440648020369068063960672322193204149535
41503128880339536053299340368006977710650566631954
81234880673210146739058568557934581403627822703280
82616570773948327592232845941706525094512325230608
22918802058777319719839450180888072429661980811197
77158542502016545090413245809786882778948721859617
72107838435069186155435662884062257473692284509516
20849603980134001723930671666823555245252804609722
53503534226472524250874054075591789781264330331690
> p13 = let xs = [ "37107287533902102798797998220837590246510135740250"
> , "46376937677490009712648124896970078050417018260538"
> , "74324986199524741059474233309513058123726617309629"
> , "91942213363574161572522430563301811072406154908250"
> , "23067588207539346171171980310421047513778063246676"
> , "89261670696623633820136378418383684178734361726757"
> , "28112879812849979408065481931592621691275889832738"
> , "44274228917432520321923589422876796487670272189318"
> , "47451445736001306439091167216856844588711603153276"
> , "70386486105843025439939619828917593665686757934951"
> , "62176457141856560629502157223196586755079324193331"
> , "64906352462741904929101432445813822663347944758178"
> , "92575867718337217661963751590579239728245598838407"
> , "58203565325359399008402633568948830189458628227828"
> , "80181199384826282014278194139940567587151170094390"
> , "35398664372827112653829987240784473053190104293586"
> , "86515506006295864861532075273371959191420517255829"
> , "71693888707715466499115593487603532921714970056938"
> , "54370070576826684624621495650076471787294438377604"
> , "53282654108756828443191190634694037855217779295145"
> , "36123272525000296071075082563815656710885258350721"
> , "45876576172410976447339110607218265236877223636045"
> , "17423706905851860660448207621209813287860733969412"
> , "81142660418086830619328460811191061556940512689692"
> , "51934325451728388641918047049293215058642563049483"
> , "62467221648435076201727918039944693004732956340691"
> , "15732444386908125794514089057706229429197107928209"
> , "55037687525678773091862540744969844508330393682126"
> , "18336384825330154686196124348767681297534375946515"
> , "80386287592878490201521685554828717201219257766954"
> , "78182833757993103614740356856449095527097864797581"
> , "16726320100436897842553539920931837441497806860984"
> , "48403098129077791799088218795327364475675590848030"
> , "87086987551392711854517078544161852424320693150332"
> , "59959406895756536782107074926966537676326235447210"
> , "69793950679652694742597709739166693763042633987085"
> , "41052684708299085211399427365734116182760315001271"
> , "65378607361501080857009149939512557028198746004375"
> , "35829035317434717326932123578154982629742552737307"
> , "94953759765105305946966067683156574377167401875275"
> , "88902802571733229619176668713819931811048770190271"
> , "25267680276078003013678680992525463401061632866526"
> , "36270218540497705585629946580636237993140746255962"
> , "24074486908231174977792365466257246923322810917141"
> , "91430288197103288597806669760892938638285025333403"
> , "34413065578016127815921815005561868836468420090470"
> , "23053081172816430487623791969842487255036638784583"
> , "11487696932154902810424020138335124462181441773470"
> , "63783299490636259666498587618221225225512486764533"
> , "67720186971698544312419572409913959008952310058822"
> , "95548255300263520781532296796249481641953868218774"
> , "76085327132285723110424803456124867697064507995236"
> , "37774242535411291684276865538926205024910326572967"
> , "23701913275725675285653248258265463092207058596522"
> , "29798860272258331913126375147341994889534765745501"
> , "18495701454879288984856827726077713721403798879715"
> , "38298203783031473527721580348144513491373226651381"
> , "34829543829199918180278916522431027392251122869539"
> , "40957953066405232632538044100059654939159879593635"
> , "29746152185502371307642255121183693803580388584903"
> , "41698116222072977186158236678424689157993532961922"
> , "62467957194401269043877107275048102390895523597457"
> , "23189706772547915061505504953922979530901129967519"
> , "86188088225875314529584099251203829009407770775672"
> , "11306739708304724483816533873502340845647058077308"
> , "82959174767140363198008187129011875491310547126581"
> , "97623331044818386269515456334926366572897563400500"
> , "42846280183517070527831839425882145521227251250327"
> , "55121603546981200581762165212827652751691296897789"
> , "32238195734329339946437501907836945765883352399886"
> , "75506164965184775180738168837861091527357929701337"
> , "62177842752192623401942399639168044983993173312731"
> , "32924185707147349566916674687634660915035914677504"
> , "99518671430235219628894890102423325116913619626622"
> , "73267460800591547471830798392868535206946944540724"
> , "76841822524674417161514036427982273348055556214818"
> , "97142617910342598647204516893989422179826088076852"
> , "87783646182799346313767754307809363333018982642090"
> , "10848802521674670883215120185883543223812876952786"
> , "71329612474782464538636993009049310363619763878039"
> , "62184073572399794223406235393808339651327408011116"
> , "66627891981488087797941876876144230030984490851411"
> , "60661826293682836764744779239180335110989069790714"
> , "85786944089552990653640447425576083659976645795096"
> , "66024396409905389607120198219976047599490197230297"
> , "64913982680032973156037120041377903785566085089252"
> , "16730939319872750275468906903707539413042652315011"
> , "94809377245048795150954100921645863754710598436791"
> , "78639167021187492431995700641917969777599028300699"
> , "15368713711936614952811305876380278410754449733078"
> , "40789923115535562561142322423255033685442488917353"
> , "44889911501440648020369068063960672322193204149535"
> , "41503128880339536053299340368006977710650566631954"
> , "81234880673210146739058568557934581403627822703280"
> , "82616570773948327592232845941706525094512325230608"
> , "22918802058777319719839450180888072429661980811197"
> , "77158542502016545090413245809786882778948721859617"
> , "72107838435069186155435662884062257473692284509516"
> , "20849603980134001723930671666823555245252804609722"
> , "53503534226472524250874054075591789781264330331690" ]
> in take 10 . show . sum $ map (read :: String -> Integer) xs
If you only want to use Int,
> p13' = let xs = [ "37107287533902102798797998220837590246510135740250"
> , "46376937677490009712648124896970078050417018260538"
> , "74324986199524741059474233309513058123726617309629"
> , "91942213363574161572522430563301811072406154908250"
> , "23067588207539346171171980310421047513778063246676"
> , "89261670696623633820136378418383684178734361726757"
> , "28112879812849979408065481931592621691275889832738"
> , "44274228917432520321923589422876796487670272189318"
> , "47451445736001306439091167216856844588711603153276"
> , "70386486105843025439939619828917593665686757934951"
> , "62176457141856560629502157223196586755079324193331"
> , "64906352462741904929101432445813822663347944758178"
> , "92575867718337217661963751590579239728245598838407"
> , "58203565325359399008402633568948830189458628227828"
> , "80181199384826282014278194139940567587151170094390"
> , "35398664372827112653829987240784473053190104293586"
> , "86515506006295864861532075273371959191420517255829"
> , "71693888707715466499115593487603532921714970056938"
> , "54370070576826684624621495650076471787294438377604"
> , "53282654108756828443191190634694037855217779295145"
> , "36123272525000296071075082563815656710885258350721"
> , "45876576172410976447339110607218265236877223636045"
> , "17423706905851860660448207621209813287860733969412"
> , "81142660418086830619328460811191061556940512689692"
> , "51934325451728388641918047049293215058642563049483"
> , "62467221648435076201727918039944693004732956340691"
> , "15732444386908125794514089057706229429197107928209"
> , "55037687525678773091862540744969844508330393682126"
> , "18336384825330154686196124348767681297534375946515"
> , "80386287592878490201521685554828717201219257766954"
> , "78182833757993103614740356856449095527097864797581"
> , "16726320100436897842553539920931837441497806860984"
> , "48403098129077791799088218795327364475675590848030"
> , "87086987551392711854517078544161852424320693150332"
> , "59959406895756536782107074926966537676326235447210"
> , "69793950679652694742597709739166693763042633987085"
> , "41052684708299085211399427365734116182760315001271"
> , "65378607361501080857009149939512557028198746004375"
> , "35829035317434717326932123578154982629742552737307"
> , "94953759765105305946966067683156574377167401875275"
> , "88902802571733229619176668713819931811048770190271"
> , "25267680276078003013678680992525463401061632866526"
> , "36270218540497705585629946580636237993140746255962"
> , "24074486908231174977792365466257246923322810917141"
> , "91430288197103288597806669760892938638285025333403"
> , "34413065578016127815921815005561868836468420090470"
> , "23053081172816430487623791969842487255036638784583"
> , "11487696932154902810424020138335124462181441773470"
> , "63783299490636259666498587618221225225512486764533"
> , "67720186971698544312419572409913959008952310058822"
> , "95548255300263520781532296796249481641953868218774"
> , "76085327132285723110424803456124867697064507995236"
> , "37774242535411291684276865538926205024910326572967"
> , "23701913275725675285653248258265463092207058596522"
> , "29798860272258331913126375147341994889534765745501"
> , "18495701454879288984856827726077713721403798879715"
> , "38298203783031473527721580348144513491373226651381"
> , "34829543829199918180278916522431027392251122869539"
> , "40957953066405232632538044100059654939159879593635"
> , "29746152185502371307642255121183693803580388584903"
> , "41698116222072977186158236678424689157993532961922"
> , "62467957194401269043877107275048102390895523597457"
> , "23189706772547915061505504953922979530901129967519"
> , "86188088225875314529584099251203829009407770775672"
> , "11306739708304724483816533873502340845647058077308"
> , "82959174767140363198008187129011875491310547126581"
> , "97623331044818386269515456334926366572897563400500"
> , "42846280183517070527831839425882145521227251250327"
> , "55121603546981200581762165212827652751691296897789"
> , "32238195734329339946437501907836945765883352399886"
> , "75506164965184775180738168837861091527357929701337"
> , "62177842752192623401942399639168044983993173312731"
> , "32924185707147349566916674687634660915035914677504"
> , "99518671430235219628894890102423325116913619626622"
> , "73267460800591547471830798392868535206946944540724"
> , "76841822524674417161514036427982273348055556214818"
> , "97142617910342598647204516893989422179826088076852"
> , "87783646182799346313767754307809363333018982642090"
> , "10848802521674670883215120185883543223812876952786"
> , "71329612474782464538636993009049310363619763878039"
> , "62184073572399794223406235393808339651327408011116"
> , "66627891981488087797941876876144230030984490851411"
> , "60661826293682836764744779239180335110989069790714"
> , "85786944089552990653640447425576083659976645795096"
> , "66024396409905389607120198219976047599490197230297"
> , "64913982680032973156037120041377903785566085089252"
> , "16730939319872750275468906903707539413042652315011"
> , "94809377245048795150954100921645863754710598436791"
> , "78639167021187492431995700641917969777599028300699"
> , "15368713711936614952811305876380278410754449733078"
> , "40789923115535562561142322423255033685442488917353"
> , "44889911501440648020369068063960672322193204149535"
> , "41503128880339536053299340368006977710650566631954"
> , "81234880673210146739058568557934581403627822703280"
> , "82616570773948327592232845941706525094512325230608"
> , "22918802058777319719839450180888072429661980811197"
> , "77158542502016545090413245809786882778948721859617"
> , "72107838435069186155435662884062257473692284509516"
> , "20849603980134001723930671666823555245252804609722"
> , "53503534226472524250874054075591789781264330331690" ]
> in take 10 . show . sum $ map ((read :: String -> Int) . take 11) xs