Earlier today I asked these three riddles based on 1729, “taxi number”. To learn about the connection between London taxis and 1729, read original post.
1. Square pair
What is the smallest number that can be expressed as the sum of a pair of squares in two different ways? Hint: it's less than 100.
Solution
12 + 72 = 52 + 52 = 50
2. Striptease
I have five wooden strips 1, 2, 7, 17 and 29 centimeters long. Any three of these stripes cannot be folded into a triangle. I would like to add another strip of wood with a maximum length of 29cm so that I still can't take three strips and make a triangle.
How many different lengths can the seventh strip have and what are they? The length must be a whole number of centimeters. As a bonus, what shape can I make using just these hypothetical extra strips?
CORRECTION: This question used to have a length of 9. This was an error. Additionally, no two lengths can be the same.
Solution 3, 4 and 5
In a triangle, the sum of the two shorter sides must be greater than the longest side. You can make a right triangle with sides of lengths 3, 4 and 5.
3. Sick Sixth
I have four numbers a, b, c, And d. These can be whole numbers or fractions.
There are six ways to multiply two such numbers: ab, cd, ac, bd, ad, bc.
The values ​​of five of these products (but not necessarily in that order) are 2, 3, 4, 5, and 6.
What is the value of the sixth product?
Solution 2.4
If we multiply ab X CD or AC X etc. or announcement X B.C. we get abcd.
Thus, there must be two pairs of 2, 3, 4, 5 and 6 whose product is the same.
The only possibility is 2 x 6 = 3 x 4 = 12. The sixth product is x 5 = 12.
Thanks to George Watkins for today's puzzles.
I've been doing puzzles here on Mondays since 2015. I'm always on the lookout for great puzzles. If you would like to offer one, write to me.
