Question

I have some beads. When I divide them into 4 equal groups, 1 bead is left. When I split one such group into 4 equal groups again, the remainder will still be 1. When I split one such groups again, the remainder is still 1. What is the minimum number of beads I have?​

Answer 1

Answer:

I have a minimum of 85 beads.

Step-by-step explanation:

Let in the final 4 groups that I have made there is only 1 bead in each.

So, the total number of beads in each of the previous groups will be (1 × 4 + 1) = 5.

Now, in each of the previous 4 groups, there are 5 beads and there is a remaining one bead.

So, the total number of beads in each of the previous groups will be (5 × 4 + 1) = 21.

Now, in each of the first 4 groups, there are 21 beads and there is a remaining one bead.

So, the total number of beads that I had initially will be (21 × 4 + 1) = 85.

Therefore, I have a minimum of 85 beads. (Answer)