School

Less than 500 pupils attend school. When it is sorted into pairs, one pupil remains. Similarly, when sorted into 3, 4, 5 and 6 members team one remains. Sorted to seven members teams, no left behind. How many pupils are attending this school?

Correct result:

n =  301

Solution:

n<500 (n1)3 (n1)4 (n1)5 (n1)6 n7 3 ...  prime number 4=22 5 ...  prime number 6=23 LCM(3,4,5,6)=2235=60  n0=LCM(3,4,5,6)=60  n1=1 n0+1=1 60+1=61 t1=n1/7=61/7=6178.7143  n2=2 n0+1=2 60+1=121 t2=n2/7=121/7=121717.2857  n3=3 n0+1=3 60+1=181 t3=n3/7=181/7=181725.8571  n4=4 n0+1=4 60+1=241 t4=n4/7=241/7=241734.4286  n5=5 n0+1=5 60+1=301 t5=n5/7=301/7=43  n6=6 n0+1=6 60+1=361 t6=n6/7=361/7=361751.5714  n7=7 n0+1=7 60+1=421 t7=n7/7=421/7=421760.1429  n8=8 n0+1=8 60+1=481 t8=n8/7=481/7=481768.7143  n=5 n0+1=5 60+1=301  d3=(n1)/3=(3011)/3=100 d4=(n1)/4=(3011)/4=75 d5=(n1)/5=(3011)/5=60 d6=(n1)/6=(3011)/6=50 d7=n/7=301/7=43



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