Cryptarithm chair

In the following addition,
TREE
LEG
LEG
LEG
—–+
CHAIR

Replace every letter with a digit to get a correct addition.
The same letter always represents the same digit and no digit is represented by 2 or more letters.

New puzzles are published at least once a month on Fridays. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars. You can check your solution here.

Pentecost

Here’s a Bongard problem for you, though I didnt mold it into the 2×6 traditional boxes:

Have a look at the following story of pentecost. I have taken it from the new King James Version, Acts 2:14-36.

The question is: in what way are the verses 17, 18, and 33 different from the other verses?

14 But Peter, standing up with the eleven, raised his voice and said to them, “Men of Judea and all who dwell in Jerusalem, let this be known to you, and heed my words.
15 For these are not drunk, as you suppose, since it is only the third hour of the day.
16 But this is what was spoken by the prophet Joel:
17 ‘And it shall come to pass in the last days, says God, That I will pour out of My Spirit on all flesh; Your sons and your daughters shall prophesy, Your young men shall see visions, Your old men shall dream dreams.
18 And on My menservants and on My maidservants I will pour out My Spirit in those days; And they shall prophesy.
19 I will show wonders in heaven above And signs in the earth beneath: Blood and fire and vapor of smoke.
20 The sun shall be turned into darkness, And the moon into blood, Before the coming of the great and awesome day of the Lord.
21 And it shall come to pass That whoever calls on the name of the Lord Shall be saved.’
22 “Men of Israel, hear these words: Jesus of Nazareth, a Man attested by God to you by miracles, wonders, and signs which God did through Him in your midst, as you yourselves also know–
23 Him, being delivered by the determined purpose and foreknowledge of God, you have taken by lawless hands, have crucified, and put to death;
24 whom God raised up, having loosed the pains of death, because it was not possible that He should be held by it.
25 For David says concerning Him: ‘I foresaw the Lord always before my face, For He is at my right hand, that I may not be shaken.
26 Therefore my heart rejoiced, and my tongue was glad; Moreover my flesh also will rest in hope.
27 For You will not leave my soul in Hades, Nor will You allow Your Holy One to see corruption.
28 You have made known to me the ways of life; You will make me full of joy in Your presence.’
29 “Men and brethren, let me speak freely to you of the patriarch David, that he is both dead and buried, and his tomb is with us to this day.
30 Therefore, being a prophet, and knowing that God had sworn with an oath to him that of the fruit of his body, according to the flesh, He would raise up the Christ to sit on his throne,
31 he, foreseeing this, spoke concerning the resurrection of the Christ, that His soul was not left in Hades, nor did His flesh see corruption.
32 This Jesus God has raised up, of which we are all witnesses.
33 Therefore being exalted to the right hand of God, and having received from the Father the promise of the Holy Spirit, He poured out this which you now see and hear.
34 For David did not ascend into the heavens, but he says himself: ‘The Lord said to my Lord, “Sit at My right hand,
35 Till I make Your enemies Your footstool.” ‘
36 “Therefore let all the house of Israel know assuredly that God has made this Jesus, whom you crucified, both Lord and Christ.”

You can check your solution here.

Quento (2)

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.

Bongard – Gospel according to Matthew

When Russian computer scientist Mikhail Moiseevich Bongard designed one hundred problems in his 1967 book on pattern recognition, he intended it to be based culture free and thus limited himself to geometry problems.

Just a quick recap: A Bongard problem has two sets of 6 boxes. The boxes on the ;left on the boxes on the right are different. What is the differende?
More precisely: Alle the boxes on the left have a common property. None of the boxes on the right have this property.

Over the past two decades the scope of Bongard problems was gradually increased from geometry to numbers and letters and words.

Here is the first of three Bongard style problemd based on the Gospel according to Matthew, using the New King James Version as published here.

Matthew 3^*/*****

You can check your solution ^here.

I’m working on a (probably free) booklet with 28 Bongard puzzles based on the gospel of Matthew. Feel free to invent more Bongard problems, and feel free to use them in your sunday school etc.