Question

What are all 6-digit natural numbers a1a2a3a4a5a6 formed by using the digits 1, 2, 3, 4, 5, 6, once each such that the number a1 a2 . . . ak is divisible by k, for 1 ≤ k ≤ 6?

Answer 1

ANSWER:-

Answer → a = 0,2,4,6.

STEP BY STEP EXPLANATION:-

→ Now if we only have to use digits 1,2,3,4,5,6 then

• → Now if we only have to use digits 1,2,3,4,5,6 thenif a = 1 then we get imperfect divisble→ 11121314/4 =2780328.5 not divisble.

• if a = 2 then 212223/3 = 70741 divisible and 21222324/4 = 5305581 divisible and 212223242526/6 = 35370540421 divisible ←Yes a=2 is also right answer.

• if a=3 then 31323334/4 = 7830833.5 not divisible.

• if a=4 then 414243/3 = 138081 & 41424344/4 = 10356086 & 414243444546/6 = 69040574091 divisible ←Yes a= 4 is also an answer.

• if a=5 then 515253 = 171751 but 51525354/4 = 12881338.5 not divisible.

• if a=6 then 616263/3 = 205421 divisible & 61626364/4=15406591 & 616263646566/6 = 102710607761 divisible ←Yes a is also 6.

HENCE, IT PROVED.

HOPE MY ANSWER HELPS YOU ❣️❣️