| date | location | Opening | − | Sacrament | = | Closing |
|---|---|---|---|---|---|---|
| July 30, 2017 | Utah | We Are All Enlisted (250) | As Now We Take the Sacrament (169) | Press Forward, Saints (81) | ||
| September 24, 2017 | Utah | Behold! A Royal Army (251) | O God, the Eternal Father (175) | God of Our Fathers, We Come unto Thee (76) | ||
| February 12, 2017 | Alberta, Canada | Come Away to the Sunday School (276) | O God, the Eternal Father (175) | Guide Me to Thee (101) | ||
| May 05, 2024 | Utah | I Know My Father Lives (302) | 'Tis Sweet to Sing the Matchless Love (177) | How Gentle God's Commands (125) | ||
| September 07, 2014 | California | Teach Me to Walk in the Light (304) | Father in Heaven, We Do Believe (180) | Be Still, My Soul (124) | ||
| May 28, 2017 | Utah | Called to Serve (249) | In Remembrance of Thy Suffering (183) | Rejoice, the Lord Is King! (66) | ||
| August 28, 2016 | Utah | The Light Divine (305) | Again We Meet Around the Board (186) | Come, We That Love the Lord (119) | ||
| October 25, 2015 | Arizona | In Our Lovely Deseret (307) | Behold the Great Redeemer Die (191) | Come, Follow Me (116) | ||
| February 12, 2017 | Wyoming | Love One Another (308) | How Great the Wisdom and the Love (195) | Our Savior's Love (113) |
Math on the Hymn Boards (Part 1)
general
When I was a teenager, my brother got up to the pulpit on during Fast and Testimony. This was a highly unusual thing for him. In fact, I can’t remember as single other time when he did that. We all recognized this and were eagerly waiting to hear him publicly bear his testimony for the first time. What he said though, no one anticipated.
“I just got up here because I wanted to point out that the hymns today are a subtraction equation. The first minus the second is the third. That’s all.”
We all quickly did the math in our head and, sure enough, he was right. I have no idea if my brother checked every week for math equations, or if he happened to notice this one. But I’ve been thinking about this recently and have been curious to see how often this happens. So, this blog post looks at math equations and other numeric patterns displayed on hymn boards. I realized though that I had way too many ideas to explore, so this will be just the first of several blog posts on this topic.
Math on three-hymn Sundays
I’ll start off with math on Sundays like the one my brother noticed, those with just three hymns. The interesting constraint about this is the sacrament hymn. Because the second hymn is almost always in the 169–196 range, that really limits how often math can occur. Let’s take a look anyway. I have data from 26,030 sacrament meetings, but for now I’ll look at the 15,184 that have just three: an opening hymn, a sacrament hymn, and a closing hymn.
I want to first start of by considering how likely something like this is. I’m going to assume we’re only using the 341 hymns in the hymnal, that a ward sings one of the 28 hymns in the 169–196 range for the sacrament hymn, and not those hymns as the opening and closing hymns. It turns out there are 4,050 ways to have a subtraction problem displayed on the hymn board. The numbers are the same for addition problems, just with the opening and closing hymns swapped. But of those, which are most likely to happen?
I cross referenced the hymn numbers from all 4,050 possibilities with the overall frequency of the hymns based on the 26,030 I have. The most likely case is
If we just consider the 341 hymns, there are actually two ways to see multiplication or division problems. It could happen by singing
I won’t bog you down with the details of other possibilities, but there are many that seem reasonably plausible. Let’s look at what actually did happen.
Subtraction
Let’s look at cases like the one in my ward that Sunday. How often do we see meetings where the opening hymn number minus the intermediate hymn number equals the closing hymn number? As it turns out, a subtraction problem was inadvertently displayed on the hymn board 9 times! Here they are:
Two things worth noting. First, as rare as this is, amazingly, two of them occurred on the same day, Februray 12th, 2017! Second, there was another worth mentioning. A ward in France sang the hymns 152, 113, and 26, which are not a math problem. But if we look at the English translations of those hymns, the hymn numbers of those three hymns do indeed make a subtraction problem! They were
Addition
Let’s move on to addition problems. Even though they’re mathematically equally probable as subtraction problems, they occurred almost twice as often as subtraction problems. Here are the nineteen instances when an additional problem was accidentally displayed on the hymn board.
| date | location | Opening | + | Sacrament | = | Closing |
|---|---|---|---|---|---|---|
| May 14, 2017 | Wyoming | More Holiness Give Me (131) | As Now We Take the Sacrament (169) | Families Can Be Together Forever (300) | ||
| March 26, 2023 | Idaho | We Thank Thee, O God, for a Prophet (19) | O God, the Eternal Father (175) | There Is a Green Hill Far Away (194) | ||
| March 01, 2015 | Utah | Be Thou Humble (130) | O Lord of Hosts (178) | Love One Another (308) | ||
| November 19, 2023 | Idaho | Lead Me into Life Eternal (45) | O Lord of Hosts (178) | Have I Done Any Good? (223) | ||
| March 29, 2015 | Northern Territory, Australia | How Great Thou Art (86) | O Lord of Hosts (178) | Hark, All Ye Nations! (264) | ||
| November 27, 2016 | Georgia | Dearest Children, God Is Near You (96) | Jesus of Nazareth, Savior and King (181) | As I Search the Holy Scriptures (277) | ||
| August 10, 2008 | Washington | Our Savior's Love (113) | We'll Sing All Hail to Jesus' Name (182) | O Love That Glorifies the Son (295) | ||
| August 28, 2016 | Nevada | Come, Follow Me (116) | God Loved Us, So He Sent His Son (187) | Keep the Commandments (303) | ||
| October 22, 2017 | Texas | The Day Dawn Is Breaking (52) | God Loved Us, So He Sent His Son (187) | Choose the Right (239) | ||
| April 30, 2017 | Utah | God of Our Fathers, Whose Almighty Hand (78) | He Died! The Great Redeemer Died (192) | I'll Go Where You Want Me to Go (270) | ||
| May 17, 2015 | California | Praise to the Man (27) | I Stand All Amazed (193) | Lord, I Would Follow Thee (220) | ||
| September 21, 2014 | California | Come, Ye Children of the Lord (58) | I Stand All Amazed (193) | Behold! A Royal Army (251) | ||
| November 12, 2023 | Ohio | All Creatures of Our God and King (62) | There Is a Green Hill Far Away (194) | As Zion's Youth in Latter Days (256) | ||
| September 04, 2016 | Utah | Rejoice, the Lord Is King! (66) | There Is a Green Hill Far Away (194) | Who's on the Lord's Side? (260) | ||
| October 09, 2016 | Utah | With Songs of Praise (71) | There Is a Green Hill Far Away (194) | Arise, O God, and Shine (265) | ||
| June 04, 2017 | Maryland | Glory to God on High (67) | Jesus, Once of Humble Birth (196) | Go Forth with Faith (263) | ||
| May 28, 2017 | Monrovia, Liberia | Sing Praise to Him (70) | Jesus, Once of Humble Birth (196) | The Time Is Far Spent (266) | ||
| May 12, 2024 | Unknown | I Need Thee Every Hour (98) | Jesus, Once of Humble Birth (196) | Love at Home (294) |
There was another case like the one in France, where the numbers when referring to their equivalents in the English hymnal, were an addition problem, but this time in Argentina. The case where the location is unknown was contributed by a person on social media, so I don’t have where they’re from.
Overall probability
So, of the 15,184 chances where math like this could happen, there was a subtraction problem 10 times and an addition problem 20 times. (I checked for the multiplication and division ones and I didn’t see any.) That means math happened about once every 506 sacrament meetings, or about once every decade or so.
Math on four-hymn Sundays
When there are four numbers to work with, the number of possible ways math could happen goes up quite a bit. I’m not a mathematician or logician, so I’m not going to entertain every concievable possibility. Instead, I’ll just focus on these four possibilities
Opening + Sacrament + Intermediate = Closing
Opening + Sacrament = Intermediate + Closing
Opening = Sacrament + Intermediate + Closing
Opening = Sacrament - Intermediate - Closing
In other words, we’re looking at either adding hymn numbers together or subtracting them and then moving the equals sign to each of the three locations. Much to my surprise, all of these possibilities are attested in my data! Let’s look at each one.
The first two is where the opening, sacrament, and intermediate hymns equal the closing hymn. This was found three times in my data:
| date | location | Opening | Sacrament | Intermediate | Closing |
|---|---|---|---|---|---|
| September 17, 2017 | England, United Kingdom | High on the Mountain Top (5) | Upon the Cross of Calvary (184) | How Firm a Foundation (85) | The Iron Rod (274) |
| February 11, 2018 | Alberta, Canada | High on the Mountain Top (5) | In Memory of the Crucified (190) | The Day Dawn Is Breaking (52) | We Love Thy House, O God (247) |
| September 08, 2024 | Idaho | Come, O Thou King of Kings (59) | 'Tis Sweet to Sing the Matchless Love (176) | Come, Listen to a Prophet's Voice (21) | As Zion's Youth in Latter Days (256) |
Next are cases where the opening plus the sacrament equal the intermediate plus the closing. This happened 25 times.
| date | location | Opening | Sacrament | Intermediate | Closing |
|---|---|---|---|---|---|
| March 24, 2013 | Utah | Awake and Arise (8) | O Savior, Thou Who Wearest a Crown (197) | Israel, Israel, God Is Calling (7) | That Easter Morn (198) |
| August 10, 2014 | South Dakota | On This Day of Joy and Gladness (64) | He Died! The Great Redeemer Died (192) | Nearer, Dear Savior, to Thee (99) | Thy Spirit, Lord, Has Stirred Our Souls (157) |
| March 15, 2015 | Iowa | Did You Think to Pray? (140) | 'Tis Sweet to Sing the Matchless Love (177) | Lead, Kindly Light (97) | Lord, I Would Follow Thee (220) |
| July 19, 2015 | Utah | Come, Sing to the Lord (10) | He Died! The Great Redeemer Died (192) | Jesus, the Very Thought of Thee (141) | Raise Your Voices to the Lord (61) |
| December 25, 2016 | Northern Territory, Australia | Hark! the Herald Angels Sing (209) | Jesus, Once of Humble Birth (196) | Joy to the World (201) | Silent Night (204) |
| March 26, 2017 | Washington | The Day Dawn Is Breaking (52) | There Is a Green Hill Far Away (194) | High on the Mountain Top (5) | Count Your Blessings (241) |
| April 09, 2017 | Virginia | Faith of Our Fathers (84) | God, Our Father, Hear Us Pray (170) | Called to Serve (249) | High on the Mountain Top (5) |
| April 30, 2017 | Utah | Abide with Me! (166) | In Remembrance of Thy Suffering (183) | On This Day of Joy and Gladness (64) | God Moves in a Mysterious Way (285) |
| June 11, 2017 | North Carolina | Master, the Tempest Is Raging (105) | Jesus, Once of Humble Birth (196) | Abide with Me! (166) | My Redeemer Lives (135) |
| July 30, 2017 | New York | Come, Come, Ye Saints (30) | With Humble Heart (171) | They, the Builders of the Nation (36) | Abide with Me; 'Tis Eventide (165) |
| July 30, 2017 | Oregon | Israel, Israel, God Is Calling (7) | As Now We Take the Sacrament (169) | God of Our Fathers, We Come unto Thee (76) | Nearer, My God, to Thee (100) |
| August 20, 2017 | Idaho | God Speed the Right (106) | We'll Sing All Hail to Jesus' Name (182) | Lead Me into Life Eternal (45) | Let Us All Press On (243) |
| August 27, 2017 | Utah | Today, While the Sun Shines (229) | As Now We Take the Sacrament (169) | Come Along, Come Along (244) | Father, This Hour Has Been One of Joy (154) |
| October 15, 2017 | Oregon | Teach Me to Walk in the Light (304) | As Now We Take the Sacrament (169) | Love One Another (308) | Abide with Me; 'Tis Eventide (165) |
| October 22, 2017 | Utah | There Is Sunshine in My Soul Today (227) | Jesus of Nazareth, Savior and King (181) | I Am a Child of God (301) | Lord, Accept Our True Devotion (107) |
| November 12, 2017 | Tennessee | All Creatures of Our God and King (62) | In Remembrance of Thy Suffering (183) | For the Beauty of the Earth (92) | Lord, We Ask Thee Ere We Part (153) |
| November 26, 2017 | Utah | We Thank Thee, O God, for a Prophet (19) | Jesus, Once of Humble Birth (196) | The Lord My Pasture Will Prepare (109) | God Speed the Right (106) |
| December 24, 2017 | Utah | Hark! the Herald Angels Sing (209) | Jesus, Once of Humble Birth (196) | Joy to the World (201) | Silent Night (204) |
| February 18, 2018 | Utah | The Lord Is My Light (89) | 'Tis Sweet to Sing the Matchless Love (176) | When Faith Endures (128) | Testimony (137) |
| May 19, 2019 | Utah | The Iron Rod (274) | Gently Raise the Sacred Strain (146) | Let the Holy Spirit Guide (143) | As I Search the Holy Scriptures (277) |
| January 08, 2023 | Idaho | Joseph Smith's First Prayer (26) | God, Our Father, Hear Us Pray (170) | The Lord Is My Light (89) | Lord, Accept Our True Devotion (107) |
| May 28, 2023 | Nevada | Redeemer of Israel (6) | Behold the Great Redeemer Die (191) | How Gentle God's Commands (125) | Praise to the Lord, the Almighty (72) |
| June 25, 2023 | Nevada | Battle Hymn of the Republic (60) | How Great the Wisdom and the Love (195) | The Lord Is My Light (89) | Abide with Me! (166) |
| January 21, 2024 | Nevada | Praise to the Lord, the Almighty (72) | Jesus of Nazareth, Savior and King (181) | Redeemer of Israel (6) | We Love Thy House, O God (247) |
| June 09, 2024 | Nevada | Guide Us, O Thou Great Jehovah (83) | Upon the Cross of Calvary (184) | Jesus, Savior, Pilot Me (104) | Lord, Dismiss Us with Thy Blessing (163) |
Last on the list additions are cases where the the opening equals the sum of the other three. This happened just once.
| date | location | Opening | Sacrament | Intermediate | Closing |
|---|---|---|---|---|---|
| September 11, 2011 | Colorado | We Are All Enlisted (250) | O God, the Eternal Father (175) | Israel, Israel, God Is Calling (7) | A Mighty Fortress Is Our God (68) |
And finally, for a subtraction-based case that isn’t equal to the others, here are the two times when the opening minus the sacrament minus the intermediate equals the closing.
| date | location | Opening | Sacrament | Intermediate | Closing |
|---|---|---|---|---|---|
| August 27, 2023 | Utah | Now Let Us Rejoice (3) | Father in Heaven, We Do Believe (180) | Dearest Children, God Is Near You (96) | Press Forward, Saints (81) |
| September 10, 2023 | Utah | O Ye Mountains High (34) | In Remembrance of Thy Suffering (183) | We Thank Thee, O God, for a Prophet (19) | Be Thou Humble (130) |
Overall probability
So, with four hymns, there are many more ways that math could happen. And it seems like it does happen every once in a while. Overall, one of these four patterns happened 31 times out of 8,640 four-hymn meetings, or in about 0.36% of them. That means, you might see one of these four about once every 6 years. So, not too unusual.
Increasing and Decreasing
The last pattern I want to look at is more just a pattern: how often are all the hymns in increasing order or in decreasing order. It turns out this is much more common than the math ones discussed above.
For Sundays with four hymns, I have 512 instances of all increasing numbers and 252 instances of all decreasing numbers. Combined, this occurs about 9% of the time, or once every 11 times you sing four hymns. So, really not too uncommon.
Just probability-wise, it’s far more likely to see all increasing numbers or all decreasing numbers on three-hymn Sundays because there are three numbers to work with instead of four. This makes sense if you think about it. The sacrament hymn will be close to the middle. (I think it’s by design so that the book is most often opened to the middle.) The opening hymn is going to be either lower than it or higher than it. As long as the closing hymn is the opposite, then we’re good. So far, I’ve seen 2,934 instances of three increasing numbers and 2,202 instances of three decreasing numbers. Combined, this occurs about 34% of the time, or once every 3 times you sing three hymns. So, really actually quite common.
For what it’s worth, the odds of this happening has gone up a little bit recently because the new hymns’ numbers are all greater than the old hymns’ numbers. It seems to occur about 3.8% more often with three-hymn Sundays and 1.2% more often with four-hymn Sundays.
Conclusion
This just a silly post that says nothing about hymns and who or why they’re chosen. But it is fun to think about possible math that could be done on the hymn numbers diplayed on the hymn board.