Question

Ben is helping plant tulips.
He plants bulbs in two rows and has one bulb left over. So he tries again.
He plants bulbs in three rows and has one bulb left over. So he tries again.
He plants bulbs in four rows and has one bulb left over. So he tries again.
He plants bulbs in five rows and has one bulb left over. So he tries again.
He plants bulbs in six rows and has one bulb left over.
We know he has less that 100 bulbs.
How many bulbs did they have?

We tried using manipulatives and became quite confused and we don't see an emerging pattern.

Answer 1

Not divisible by 2,3,5. Which means it is not divisible by any number that is divisible by any of these (ie, 2,4,6,8,9,10,12...

so look at the possibilities
start with 6 rule+1
7,13,19,25,31,37,43,49,55,61,...
now eliminate those the five rule+1 eliminates and you are left with..
31,61
now eliminate those that four rule+1
and 61 is left, and it satisfies the three rule, and the two rule.