Q: At a zoo, the number of two-legged birds is twice the number of 4-legged mammals.

If there is a total of 80 legs, how many birds and how many 4-legged mammals are there?

A: There are 20 two-legged birds (40 legs) and 10 four-legged mammals (40 more legs).
Let x = the number of 4-legged mammals
then 2x = # of 2-legged birds
2x(2) + x (4) = 80
8x = 80
x = 10 2x = 20

Q: A palindromic number is like a palindrome word (like “kayak”) which reads the same forwards and backwards. Find all the 3 digit palindromic numbers that are multiples of 18 (see if you can find a clever way of doing this).

A: There are 4 numbers that meet this criteria: 252, 414, 666, 828

Any and all multiples of 18 have to be multiples of 9 and also have to be even so the number must end with a 2, 4, 6 or 8 which means that it must also begin with a 2, 4, 6 or 8 as the number is palindromic.

Looking at 3 digit numbers that begin and end with 2 whose digits add up to 9 or a multiple of 9 only yields 252.

Looking at 3 digit numbers that begin and end with 4 whose digits add up to 9 or a multiple of 9 only yields 414.

Looking at 3 digit numbers that begin and end with 4 whose digits add up to 9 or a multiple of 9 only yields 414.

Looking at 3 digit numbers that begin and end with 6 whose digits add up to 9 or a multiple of 9 only yields 666.

Looking at 3 digit numbers that begin and end with 4 whose digits add up to 9 or a multiple of 9 only yields 828.

https://www.theguardian.com/science/alexs-adventures-in-numberland/2014/oct/27/solutions-to-martin-gardners-best-mathematical-puzzles

Q: What is the longest sum of consecutive positive integers that sum to 2025?

A: The longest is 54 numbers from 11 til 64 (including 11 and 64).
If we add 11 and 64, we get 75.
The adjacent numbers to 11 and 64 that also add up to 75 like 12 and 63.
There are 27 pairs of numbers that add up to 75 — all those numbers sum to 2025.