William, Count of Luxembourg
William I, Count of Luxembourg( 1081–1131) was count of Luxembourg( 1096 – 1131), in succession to his elder brother Henry III of Luxembourg.
They were both sons of Conrad and Clementia of Aquitaine.
William was the first of his family to use the title" count of Luxembourg" in his documents.
Like his predecessors, he was embroiled in debates with the archbishop of Trier Bruno in 1122 and 1127, leading to William's excommunication.
Around 1105 he married Mathilde or Luitgarde of Northeim, daughter of Kuno, count of Beichlingen, and had three children:
Henry IV, Count of Holstein-Rendsburg
Henry IV, Count of Holstein- Rendsburg( 1397 – 28 May 1427) was Count of Holstein- Rendsburg and Duke of Schleswig from 1404 until his death.
Godfrey I, Count of Namur
Godfrey of Namur (attested in 1080; died 19 August 1139) was a Lotharingian nobleman.
He was Count "jure uxoris" of Porcéan from 1097 until his death.
From 1102, he was also Count of Namur.
He was the oldest son of Count Albert III and his wife Ida of Saxony, the heiress of Laroche.
In 1121, he founded Floreffe Abbey, where he also was buried.
Tjuyu
Tjuyu( sometimes transliterated as Thuya or Thuyu) was an Egyptian noblewoman and the mother of queen Tiye, and the wife of Yuya.
She is the grandmother of Akhenaten, and great grandmother of Tutankhamun.
Beatrice of Luxembourg
Beatrice of Luxembourg( 1305 – 11 November 1319), was by birth member of the House of Luxembourg and by marriage Queen of Hungary.
She was the youngest child of Henry VII, Holy Roman Emperor and his wife, Margaret of Brabant.
Her two siblings were John of Luxembourg and Marie of Luxembourg, Queen of France.
Adelaide of Ballenstedt
Adelaide of Ballenstedt( after 1139) was the daughter of Otto of Ballenstedt and a member of the House of Ascania.
She married, successively, Henry IV, Count of Stade, and Werner, Count of Osterburg.
Hubba bint Hulail
Hubba bint Hulail was the grandmother of Hashim ibn' Abd Manaf, thus the great- great- great- grandmother of the Islamic" Nabī"( Prophet) Muhammad ibn Abdullah.
Hannah Arnold
Hannah Arnold, also known as Hannah Waterman King, was the grandmother of Benedict Arnolds children.
Alice of Namur
Alice of Namur( died July 1169 at Valenciennes) was the daughter of Godfrey I, Count of Namur and Ermesinde, Countess of Luxembourg and Longwy the daughter of Conrad I of Luxembourg.
Her father married her off to Baldwin IV, Count of Hainault around 1130.
Gislebert of Mons described her as having" a graceful body and a beautiful face".
Her son was the heir of Namur when her brother Henry IV of Luxembourg died in 1196.
Her children with Baldwin IV of Hainaut were:
She was buried inside Saint Waltrude Collegiate Church.
Henry IV, Count of Luxembourg
Henry IV (– 14 August 1196), called the Blind ("l'Aveugle" or "der Blinde"), was count of Luxembourg from 1136 until his death and count of Namur (as Henry I) from 1139 until his abdication in 1189.
He was the son of Godfrey I, Count of Namur and Ermesinde, a daughter of Conrad I of Luxembourg.
He inherited the counties of La Roche and Durbuy from his cousins Henry II of Durbuy and Henry of Laroche.
When another cousin, Conrad II of Luxembourg, died he was granted that county by the Emperor Lothair II, who thus prevented its passing to the French count of Grandpré.
At the same time he also inherited the advocacies of the abbeys of Saint-Maximin at Trier and Saint-Willibrord at Echternach.
This was the cause of many conflicts with Albero of Montreuil, archbishop of Trier.
Three years later, he inherited Namur from his father.
In 1141, he helped Alberon II, Bishop of Liège take Bouillon with Renaut I of Bar.
In 1147, he gave up Saint-Maximin, but he regained it on the death of Archbishop Albero de Montreuil in 1152.
The new archbishop, Hillin of Falmagne, exchanged the rights over the abbeys with the town of Grevenmacher in 1155.
In 1157, he married Laurette (d.1175), daughter of Thierry of Alsace, Count of Flanders, and Margaret of Clermont.
They separated in 1163.
Left without child, he designated his brother-in-law Baldwin IV of Hainault, husband of his sister Alice of Namur, as his heir.
When Baldwin died in 1171, he designated Baldwin V. Baldwin V and Henry carried out two wars, in 1170 and 1172, with Henry III of Limburg.
In 1171, Henry married a second time, this time to Agnes, daughter of Henry I, Count of Guelders and Agnes of Arnstein.
Heirless still, he repudiated her in 1184, but fell seriously ill and rejoined her.
In September 1186, a girl, Ermesinde, was born to them.
This birth called into question the plan of succession, as Henry considered his promise to Baldwin null and void.
Henry, then 76 years old, pledged his daughter in marriage to Henry II of Champagne.
Baldwin still claimed his inheritance.
It was then decided that Baldwin would inherit Namur, Ermesinde would inherit Durbuy and La Roche, and Luxembourg ("fief masculin") would revert to the Empire.
The fiefs were dispensed in 1189.
After the planned marriage between Ermesinde and the count of Champagne was cancelled, Henry betrothed her instead to Theobald I of Bar.
He entered into a war with Henry of Limburg and was defeated on 1 August 1194 at Noville-sur-Mehaigne.
He died two years later in Echternach.

Question: Who is the paternal grandmother of Henry Iv, Count Of Luxembourg?
Answer: Ida of Saxony