In august 2020 I published a couple of puzzles which in the Dutch daily newspaper Algemeen Dagblad (ad.nl) are called Quento.
On the left side you see some numbers and arithmetic signs. On the right you see a couple of ‘answers’. Your task is to make valid calculations by travelling through the grid and ending up with one of the answers.
Of course there is a website, and an app for both Android and Ipad. Personally I think the exercises are too easy, though no doubt they can be increased by adding size and moving to higher numbers, as shown in our 4th problem. In the app I did see higher numbers, in the sense of multiples of 3, 4, 5 , and so on, but I didn’t see larger sizes, as in our fourth problem. That may be because I didn’t purchase the app and just used the free version.
Quento 5*/*****
Quento 6*/*****
Quento 7*/*****
You can check your solutions at here.
Some thoughts about Quento
1) The problem “find the exercise leading to the answer” sounds like it is a problem in inductive logic. But alas it is not. There are a very finite number of routes leading to a possible answer.
2) A good question is: how many routes are the through a 3×3 grid? Or more general how many routes are there through an nxm grid?
Let’s start with a 2×2 grid, consisting of four numbers and foru +/- signs in between the numbers.
If we have them arranged as
A+B
+ +
C+D,
we have A+B, A+C, B+D and C+D or 4 routes. For every minus sign we do not just have A-B, but also B-A, giving an extra 4 routes of length 2, making 4-8 routes of length 2.
In addition, there are 4 routes of length 3, and 1 route of length 4 ( taking only + signs).
With minus signs, there are an additional 4 routes of length 3, but suddenly 4 of length 4.
That gives a total of 4-8 routes of length 2, 4-8 routes of length 3, and 1-5 routes of length 4, making 17 in total.
justpuzzles 