These triplets of numbers can be linked in a very specific way:

• 1, 32, 88
• 9, 19, 87
• 11, 93, 97
• 13, 28, 98
• 18, 91, 97
• 19, 87, 95
• 27, 38, 98
• 27, 88, 93
• 33, 38, 88

For the integers 1-99 inclusive, these triplets are not unique. What is:

1. the smallest such triplet?
2. the largest such triplet?
3. the only consecutive triplet?

(NB: only triplets with three different numbers are considered valid).

So the triplets can be linked in a very specific way:

1, 32, 88 becomes THIRTYTWONEIGHTYEIGHT - it can be written around in a circle with first and last letters linking up

The smallest triplet is:

1, 2, 8 = ONEIGHTWO

The largest is:

87, 97, 99 = NINETYNINEIGHTYSEVENINETYSEVEN

And the only consecutive one is:

8, 9, 10 = EIGHTENINE

Credits to J. Siebeneichler for most of the inspiration, if you upvoted this answer go upvote theirs as well.

• If someone could add a visual, that would be great. I don't have access to graphics software at the moment. Commented Dec 25, 2017 at 8:30

The link between the numbers is:

The first letter of the first number spelled out is the last letter of the second number spelled out, and the last letter of the first number is first letter of the last number.

Given the third request, I think it's reasonable to assume that

the second number is always greater than the first, and the third always greater than the second.

Assuming that smallest and largest refer to their sum:

The smallest such triplet:

one, two, eight

The largest such triplet:

ninety-seven, ninety-seven, ninety-nine

The only consecutive triplet:

eight, nine, ten... or nine, ten, eleven, so there must be another condition to the connection

• Close. Your assumption is wrong and the largest triplet is wrong. Showing the triplets in exactly the right format should help you get the full answer. Commented Dec 23, 2017 at 21:56
• See my clarification to the question. The largest is still wrong, and your other consecutive example doesn't work at all. The last point of my previous comment is very important (think spatially). Commented Dec 24, 2017 at 20:09