Did you solve it? The London taxi that entered history | mathematics
Earlier today, I assigned these three mysteries, loosely based on the year 1729, to “The Taxi Number.” To read more about the link between London taxis and 1729, please read the 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? Note: less than 100
solution
12 + 72 = 52 + 52 = 50
2. Strip tease
I have five strips of wood in lengths of 1, 2, 7, 17 and 29 cm. It is impossible to arrange any of these three strips into a triangle. I want to add another strip of wood with a maximum length of 29cm, so that I can’t take three strips and make a triangle.
How many different lengths of the seventh bar are possible, and what are they? Lengths must be an integer number of centimetres. As a bonus, what look can I create using just these virtual extra strips?
Correction: This question was previously 9. This was an error. Also, no two lengths can be the same.
solution 3, 4 and 5
In a triangle, the sum of the two smaller sides must be greater than the longer side. You can create a right triangle with side lengths 3, 4, and 5.
3. The sixth patient
I have four numbers A, B, C, and D. They may be integers or fractions.
There are six ways to multiply two of these numbers together: AB, CD, AC, BD, AD, BC.
The values for five of these products, but not necessarily in this order, are 2, 3, 4, 5, and 6.
What is the value of the sixth product?
solution 2.4
If we double dad S CD or AC current S Bahraini dinar or advertisement S B.C.E. We get it abcd.
Hence there must be two pairs of 2 and 3 and 4 and 5 and 6 whose product is the same.
The only possibility is 2 x 6 = 3 x 4 = 12. 6th product x 5 = 12.
Thanks to George Watkins for today’s puzzles.
I’ve been doing puzzle here on Alternate Mondays since 2015. I’m always on the lookout for great puzzles. If you would like to suggest one, email me.