Wily Winifred and the Case of the Odd Numbers

Mrs. Shine was having a rough day and wanted a break. So she asked her class to calculate the sum of the first 50 odd numbers. In a few moments, Winifred was at her desk with the correct answer of 2,500. Stunned, Mrs. Shine figured she must have gotten lucky, and sent precocious Winifred back to her seat with the task of finding the sum of the first 75 odd numbers. Again, Winifred returned in seconds with the correct answer (5,625).

How did Winifred find the answer so quickly?

Winifred, being the precocious child she is, realized there was a pattern when computing smaller sums of odd numbers.

First 3: 1 + 3 + 5 = 9
First 4: 1 + 3 + 5 + 7 = 16
First 5: 1 + 3 + 5 + 7 + 9 = 25

Do you see the pattern like our dear friend Winnie?

For the first n odd numbers, the sum is equal to n2. Thus the first 50 is 502, or 2,500, and the first 75 is 752, or 5,625.

Posted in Brain Teasers

Take Away All My Letters

Take away my first letter and I remain the same. Take away my last letter and I remain unchanged. Remove all my letters and I’m still me.

What am I?

A mail carrier. Letters in this sense are envelopes rather than the letters of the alphabet.

Posted in Riddles

What Letter Comes Next MAMJJASO

What letter comes next in this sequence?

M, A, M, J, J, A, S, O, ____

N. The letter represent the first letters of the months of the year, starting with March. N is for November, and of course D would be the next one.

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Don’t Speak But No Word I Cannot Make

I don’t speak but there is no word I cannot make. What am I?

The alphabet.

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Same Three Digits with Sum of 800

When Florence and Willie finished playing darts, they proudly announced that their 3-digit scores added up to exactly 800 points. Furthermore, each of their scores shared the same 3 digits, without any repeating digits.

What were their two scores?

364 and 436.

You could figure this out mathematically, but instead, I plugged in digits that added up to 10 for the first column, 9 for the second column (since you carry the 1) and 7 for the third column (again, because you’re carrying the 1).

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Pronounced As One Letter, Written With Three

Pronounced as one letter,
And written with three,
Two letters there are,
And two only in me.
I’m double, I’m single,
I’m black, blue, and gray,
I’m read from both ends,
And the same either way.

What am I?

Eye. It’s pronounced like the letter ‘i’, but written with three letters. There are only two letters used (‘e’ and ‘y’). The eye is double with two ‘e’s and represents a single eye. The eye is made up of various colors, some of which are black, blue and gray. And lastly, the eye is a palindrome, spelled the same forward and backward.

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What Do You Serve?

What do you serve that a polite recipient would immediately send back?

A ball, when you’re playing tennis, volleyball, table tennis, etc.

Posted in Riddles

Two Three Four Fifteen

What is the missing number?

2 3 4 15 12
3 4 5 28 20
4 5 6 45 30
5 6 7 66 42
6 7 8 ?? 56

91. To get the number in the fourth column, you add the numbers in column 1 and 2, then multiply by the number in column 2. f(n,m) = (n + m) * m
For example, f(2,3) = (2 + 3) * 3 = 15. Thus f(6,7) = (6 + 7) * 7 = 91

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How Far Does a Dog Walk?

How far can a blind dog walk into a forest?

Halfway. After he gets halfway, he’s walking out of the forest.

Posted in Riddles

The Potato Paradox

Fred brings home 100 pounds of potatoes, which (being purely mathematical potatoes) consist of 99 percent water. He then leaves them outside overnight so that they consist of 98 percent water. What is their new weight?

50 pounds.

100 lb of potatoes with 99% water weight means there’s 99 lb of water and 1 lb of solids, a 1:99 ratio.

If the water decreases to 98%, then the solids account for 2% of the weight. The 2:98 ratio reduces to 1:49. Since the solids still weigh 1 lb, the water must weigh 49 lb for a total of 50 lbs for the answer.

Read more at the Potato Paradox wikipedia page.

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