Three Clues and a Number Trivia Quiz

Answer: 99

Combining the three clues, we were looking for an odd two digit number larger than the largest even two digit number.

The largest even two digit number is 98, which means we were looking for 99.

Answer: 500

Combining the three clues, we were looking for a three digit number evenly divisible by 5 which has at least two similar digits.

In order for a number to be evenly divisible by 5, its last digit must be either 0 or 5. This rules out 222 and 551.

From the remaining options, both multiples of 5, only the number 500 has at least two similar digits. Sorry, 125.

Answer: 12

Combining the three clues, we were looking for a number smaller than 500 whose digits are consecutive in ascending order and which represents the number of numbers smaller than 500 with their digits consecutive in ascending order. To be consecutive in ascending order means they must have at least two digits.

A bit more tricky, but all it takes is following the rules.

Write down the numbers which satisfy the clues: 12, 23, 34, 45, 56, 67, 78, 89, 123, 234, 345, 456.

Now count them. 12 numbers in total.

Answer: None of these

Combining the three clues, we were looking for a seven digit square number with its last digit being 7.

Here's the deal - if you square a number, the last digit of the result is always the number 1, 4, 5, 6, 9 or an even number of zeroes. No digit squared results in a number ending with 7.

So, to be honest, not only 1234567, 1000007 and 7777777 are wrong answers - there are no seven digit square numbers ending with 7 because, in fact, there are no square numbers ending with 7 at all.

Answer: 6666

Combining the three clues, we were looking for a four digit palindromic number, which remains palindromic if you omit its first digit.

The clues can only be satisfied by a number whose digits are all identical, hence 6666 was our goal.

Answer: 91

Combining the three clues, we were looking for a two digit number evenly divisible by both 7 and 13.

The smaller such number is 91, the product of 7 and 13. The next one, 182, is a three digit number and so does not fit all of the clues.

Answer: 52

Combining the three clues, we were looking for a two digit number which is one third of the product of two consecutive numbers, and if reversed becomes a square number.

This one is a bit more difficult. 49 and 71 are ruled out because their reverse is not a square number. the reverse of 18 is a square number (81), but it is a third of 54 which does not satisfy the requirement of being the product of two consecutive numbers.

Only 52 meets all conditions, as its reverse is 25 and is a third of 156 which is the product of 12 and 13.

Answer: 31

Combining the three clues, we were looking for a prime number, which remains prime if reversed, with the reverse of its square being the square of its reverse.

Once you figure out the linguistic part, it becomes clearer.

Only 31 and 17 satisfy the condition that their reverse is also prime.

Only with 31 and 13 the square rule neatly applies - 31 squared is 961 which is the reverse of 169, which is the square of... 13.

Answer: 9876543210

Combining the three clues, we were looking for a ten digit number which does not have two consecutive even digits and does not have recurring digits.

This one is all about concentration.

I hope you kept your heads and eyes straight and figured out that the only correct option was 9876543210.

Answer: 142857

Let us refrain from combining the three clues this time because it could get awkward.

542917 and 333333 should be ruled out without going through calculation, because multiplying them by 7 can not yield a six digit number.

102500 is ruled out because doubling it yields 205000, nearly the same digits as the original but not quite.

The correct answer is the fun part:

142857 x 2 = 285714
142857 x 7 = 999999

And there's more:

142857 x 3 = 428571
142857 x 4 = 571428
142857 x 5 = 714285
142857 x 6 = 857142