+19 Find the number of 7-digit positive integers, where the product of the digits is equal to 10000.
+2863 This is a prime factoring combination problem
EDIT: SEE Electric Pavlov's reply below!!!!!!!!!!!
Prime factorize 10,000
that is 24 * 54
Notice how it is 2 * 2 * 2 * 2 * 5 * 5 * 5 * 5
Since there are 8 numbers, and you want 7 digits, there is only one way to eliminate.
It is now 10 * 2 * 2 * 2 * 5 * 5 * 5
There can only be one 10, three 2, three 5s.
So how many unique ways can we arrange these?
Lets do some case work
10 2 2 2 5 5 5
How many ways can you arrange (three 2s and three 5s)
+
2 10 2 2 5 5 5
How many ways can you arrange (one 10 two 2 and three 5s)
+
5 10 2 2 2 5 5
How many ways can you arrange (one 10 three 2 and two 5s)
After adding the number of cases together, you should get your answer. I will leave you to solve that.
+37146 Not sure why you eliminated digits by using a 10.....it is still 8 digits long
why wouldn't you use '4 ' by using two 2's
example 4 2 2 5555 = 10000
a=1;b=1;c=1;d=1;e=1;f=1;g=1;p=0; cycle:if(a*b*c*d*e*f*g==10000, goto loop, goto next); loop:print a*1000000+b*100000+c*10000+d*1000+e*100+f*10+g," ",;p=p+1; next:g++;if(g<10, goto cycle, 0);g=1;f++;if(f<10, goto cycle, 0);g=1;f=1;e++;if(e<10, goto cycle,0);g=1;f=1;e=1;d++;if(d<10, goto cycle,0);g=1;f=1;e=1;d=1;c++;if(c<10, goto cycle,0);g=1;f=1;e=1;d=1;c=1;b++;if(b<10, goto cycle,0);g=1;f=1;e=1;d=1;c=1;b=1;a++;if(a<10, goto cycle, 0);print"Total = ",p.
You can do it in a simple:2 x 7!/2!4! + 7!/4!= 420 numbers.
1255558 1255585 1255855 1258555 1285555 1445555 1454555 1455455 1455545 1455554 1525558 1525585 1525855 1528555 1544555 1545455 1545545 1545554 1552558 1552585 1552855 1554455 1554545 1554554 1555258 1555285 1555445 1555454 1555528 1555544 1555582 1555825 1555852 1558255 1558525 1558552 1582555 1585255 1585525 1585552 1825555 1852555 1855255 1855525 1855552 2155558 2155585 2155855 2158555 2185555 2245555 2254555 2255455 2255545 2255554 2425555 2452555 2455255 2455525 2455552 2515558 2515585 2515855 2518555 2524555 2525455 2525545 2525554 2542555 2545255 2545525 2545552 2551558 2551585 2551855 2552455 2552545 2552554 2554255 2554525 2554552 2555158 2555185 2555245 2555254 2555425 2555452 2555518 2555524 2555542 2555581 2555815 2555851 2558155 2558515 2558551 2581555 2585155 2585515 2585551 2815555 2851555 2855155 2855515 2855551 4145555 4154555 4155455 4155545 4155554 4225555 4252555 4255255 4255525 4255552 4415555 4451555 4455155 4455515 4455551 4514555 4515455 4515545 4515554 4522555 4525255 4525525 4525552 4541555 4545155 4545515 4545551 4551455 4551545 4551554 4552255 4552525 4552552 4554155 4554515 4554551 4555145 4555154 4555225 4555252 4555415 4555451 4555514 4555522 4555541 5125558 5125585 5125855 5128555 5144555 5145455 5145545 5145554 5152558 5152585 5152855 5154455 5154545 5154554 5155258 5155285 5155445 5155454 5155528 5155544 5155582 5155825 5155852 5158255 5158525 5158552 5182555 5185255 5185525 5185552 5215558 5215585 5215855 5218555 5224555 5225455 5225545 5225554 5242555 5245255 5245525 5245552 5251558 5251585 5251855 5252455 5252545 5252554 5254255 5254525 5254552 5255158 5255185 5255245 5255254 5255425 5255452 5255518 5255524 5255542 5255581 5255815 5255851 5258155 5258515 5258551 5281555 5285155 5285515 5285551 5414555 5415455 5415545 5415554 5422555 5425255 5425525 5425552 5441555 5445155 5445515 5445551 5451455 5451545 5451554 5452255 5452525 5452552 5454155 5454515 5454551 5455145 5455154 5455225 5455252 5455415 5455451 5455514 5455522 5455541 5512558 5512585 5512855 5514455 5514545 5514554 5515258 5515285 5515445 5515454 5515528 5515544 5515582 5515825 5515852 5518255 5518525 5518552 5521558 5521585 5521855 5522455 5522545 5522554 5524255 5524525 5524552 5525158 5525185 5525245 5525254 5525425 5525452 5525518 5525524 5525542 5525581 5525815 5525851 5528155 5528515 5528551 5541455 5541545 5541554 5542255 5542525 5542552 5544155 5544515 5544551 5545145 5545154 5545225 5545252 5545415 5545451 5545514 5545522 5545541 5551258 5551285 5551445 5551454 5551528 5551544 5551582 5551825 5551852 5552158 5552185 5552245 5552254 5552425 5552452 5552518 5552524 5552542 5552581 5552815 5552851 5554145 5554154 5554225 5554252 5554415 5554451 5554514 5554522 5554541 5555128 5555144 5555182 5555218 5555224 5555242 5555281 5555414 5555422 5555441 5555812 5555821 5558125 5558152 5558215 5558251 5558512 5558521 5581255 5581525 5581552 5582155 5582515 5582551 5585125 5585152 5585215 5585251 5585512 5585521 5812555 5815255 5815525 5815552 5821555 5825155 5825515 5825551 5851255 5851525 5851552 5852155 5852515 5852551 5855125 5855152 5855215 5855251 5855512 5855521 8125555 8152555 8155255 8155525 8155552 8215555 8251555 8255155 8255515 8255551 8512555 8515255 8515525 8515552 8521555 8525155 8525515 8525551 8551255 8551525 8551552 8552155 8552515 8552551 8555125 8555152 8555215 8555251 8555512 8555521 Total = 420
