## 3 squares

I’ve pinched this from the old ToM site.

There are three distinct integers which have the property that the sum of any two of them is a perfect square. What are they ?

There is more than one solution.

Posted by Chris under MathsChallenge (8 Responds)

I’ve pinched this from the old ToM site.

There are three distinct integers which have the property that the sum of any two of them is a perfect square. What are they ?

There is more than one solution.

Posted by Chris under MathsChallenge (36 Responds)

It’s ages since I’ve seen this one.

After flipping two coins, at least one of them shows heads. What is the probability that the other one also shows heads?

Posted by Chris under MathsChallenge (30 Responds)

If the probability of an event happening in one trial is p, the average number of trials needed to get the event is 1/p. Prove it.

Posted by Chris under Tom (8 Responds)

n people are standing in a queue. On average, how many of them can (truthfully) say that they are taller than everyone ahead of them?

NB The person at the front of the queue, can say that he is taller than everyone ahead of him. Assume that they are able to accurately determine their heights.

Posted by Chris under MathsChallenge (18 Responds)

Five schoolchildren were weighed in pairs. Their (combined) weights were:

129, 125, 124, 123, 122,121, 120, 118, 116 and 114 lbs. What were their individual weights?

I) 1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, …

II) 1, 2, 4, 8, 16, 31, … (not 32)

III) 1, 25, 23, 13, 3, 14, 15, 16, 8, …

Posted by Karys under Tom (5 Responds)

In a 6×6 grid of crosses :

**x x x x x x
x x x x x x
x x x x x x
x x x x x x
x x x x x x
x x x x x x**

1) Remove 6 xs, so that in each column and each row has an even number of xs. Try removing 8 xs instead of 6.

2) How many such possible combinations are there ?

Posted by TheWyvern under SharedPuzzle (11 Responds)

how could we measure the speed of light from holy book (Any holy book .i.e. the holy qur’an – the bible …etc)..but the proof from within it’s verses ..?! of course the Proof will mainly depend on scientific explanation to get the speed of light .

Posted by Karl Sharman under Tom (14 Responds)

What is the 5-digit number in which the sum of the first two digits is one smaller than the third, the third is double the fourth, the fourth is double the last, the third is the product of the fourth and fifth, the second is five more than the first, and the first is one-eighth the third and also one-fourth of the fourth?

Tags: Mathemagic
Posted by Karl Sharman under Tom (4 Responds)

Can you decode the following well known saying. Each encoded letter represents more than one real letter:

B DBBCC, DBADABCDA B AC