For mathematicians, satisfying a problem’s necessary conditions is required before the problem can be solved, and satisfying its sufficient conditions guarantees the problem’s solution. Concerning Jesus’ atoning sacrifice on the cross, Hebrews 10:1–18 triumphantly proclaims that, unlike the sacrifices prescribed in Leviticus, our Lord’s sacrifice was not only necessary but entirely sufficient for the atonement of our sins, reconciling us to God. Verses 1–4 proclaim that the Old Testament sacrifices of bulls and goats were “but a shadow of the good things to come,” could “never … make perfect,” and were inadequate “to take away sins.” These sacrifices were ineffective because they did not satisfy the necessary conditions of the problem of sin. Furthermore, they were insufficient, repeated yearly, reminding people they were still sinners estranged from God. Verses 5–7 draw our attention to Psalm 40:6–8, in which we are told it was God’s plan that animal sacrifices were to point toward an ultimate sacrifice. Jesus, who came in the flesh and died on the cross in our stead, became that ultimate sacrifice. And by His once-and-for-all-time sacrifice, the promise of remission of sins and a renewed relationship with the Father was secured. That is God’s promise of the new covenant, written on believers’ hearts, made in Jeremiah 31, and repeated in Hebrews 10:11–18. That promise was fulfilled in Jesus’ death. His atoning sacrifice was necessary and sufficient, completely and totally efficacious in atoning for our sins. So why, after placing your faith in Christ, would you follow a religion that requires sacrifices that are never efficacious? Why, after enjoying God’s grace, would you turn your back on that grace attempting to earn God’s favor, which can never be accomplished? That is what the writer to the Hebrews is asking. Yet that is what we do when we think that God will not accept us unless we try harder, behave better, or perform good deeds to make up for wrongs. We must remember that everyone who trusts in Jesus Christ alone for salvation is forgiven his sins and brought into a right relationship with God. What has been accomplished by Christ need never be repeated, for it was necessary, sufficient, and totally efficacious in solving the problem of our sin and estrangement from God.